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Analysis of Markov chain approximation for Asian options and occupation-time derivatives: Greeks and convergence rates Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2021-01-15 Wensheng Yang, Jingtang Ma, Zhenyu Cui
The continuous-time Markov chain (CTMC) approximation method is a powerful tool that has recently been utilized in the valuation of derivative securities, and it has the advantage of yielding closed-form matrix expressions suitable for efficient implementation. For two types of popular path-dependent derivatives, the arithmetic Asian option and the occupation-time derivative, this paper obtains explicit
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Integro-differential optimality equations for the risk-sensitive control of piecewise deterministic Markov processes Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2021-01-07 O. L. V. Costa, F. Dufour
In this paper we study the minimization problem of the infinite-horizon expected exponential utility total cost for continuous-time piecewise deterministic Markov processes with the control acting continuously on the jump intensity \(\lambda \) and on the transition measure Q of the process. The action space is supposed to depend on the state variable and the state space is considered to have a frontier
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Considerations on the aggregate monotonicity of the nucleolus and the core-center Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2021-01-06 Miguel Ángel Mirás Calvo, Carmen Quinteiro Sandomingo, Estela Sánchez-Rodríguez
Even though aggregate monotonicity appears to be a reasonable requirement for solutions on the domain of convex games, there are well known allocations, the nucleolus for instance, that violate it. It is known that the nucleolus is aggregate monotonic on the domain of essential games with just three players. We provide a simple direct proof of this fact, obtaining an analytic formula for the nucleolus
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Portfolio selection with drawdown constraint on consumption: a generalization model Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2021-01-06 Junkee Jeon, Kyunghyun Park
In this study, we generalize the results of Arun (The Merton problem with a drawdown constraint on consumption. Working paper, 2013) on the optimal consumption and investment problem of an infinitely lived agent who does not accept her consumption falling below a fixed proportion of her historically highest level, the so-called drawdown constraint on consumption. We extend the results to a general
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An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-11-18 Yekini Shehu, Olaniyi S. Iyiola, Duong Viet Thong, Nguyen Thi Cam Van
The paper introduces an inertial extragradient subgradient method with self-adaptive step sizes for solving equilibrium problems in real Hilbert spaces. Weak convergence of the proposed method is obtained under the condition that the bifunction is pseudomonotone and Lipchitz continuous. Linear convergence is also given when the bifunction is strongly pseudomonotone and Lipchitz continuous. Numerical
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On the computation of Whittle’s index for Markovian restless bandits Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-11-11 Urtzi Ayesta, Manu K. Gupta, Ina Maria Verloop
The multi-armed restless bandit framework allows to model a wide variety of decision-making problems in areas as diverse as industrial engineering, computer communication, operations research, financial engineering, communication networks etc. In a seminal work, Whittle developed a methodology to derive well-performing (Whittle’s) index policies that are obtained by solving a relaxed version of the
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A multi-objective approach for PH-graphs with applications to stochastic shortest paths Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-10-24 Peter Buchholz, Iryna Dohndorf
Stochastic shortest path problems (SSPPs) have many applications in practice and are subject of ongoing research for many years. This paper considers a variant of SSPPs where times or costs to pass an edge in a graph are, possibly correlated, random variables. There are two general goals one can aim for, the minimization of the expected costs to reach the destination or the maximization of the probability
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Interplay of non-convex quadratically constrained problems with adjustable robust optimization Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-10-06 Immanuel Bomze, Markus Gabl
In this paper we explore convex reformulation strategies for non-convex quadratically constrained optimization problems (QCQPs). First we investigate such reformulations using Pataki’s rank theorem iteratively. We show that the result can be used in conjunction with conic optimization duality in order to obtain a geometric condition for the S-procedure to be exact. Based upon known results on the S-procedure
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A transformation-based discretization method for solving general semi-infinite optimization problems Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-09-22 Jan Schwientek, Tobias Seidel, Karl-Heinz Küfer
Discretization methods are commonly used for solving standard semi-infinite optimization (SIP) problems. The transfer of these methods to the case of general semi-infinite optimization (GSIP) problems is difficult due to the \(\mathbf {x}\)-dependence of the infinite index set. On the other hand, under suitable conditions, a GSIP problem can be transformed into a SIP problem. In this paper we assume
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A numerical approach to solve consumption-portfolio problems with predictability in income, stock prices, and house prices Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-09-19 Farina Weiss
In this paper, I establish a numerical method to solve a generic consumption-portfolio choice problem with predictability in stock prices, house prices, and labor income. I generalize the SAMS method introduced by Bick et al. (Manag Sci 59:485–503, 2013) to state-dependent modifiers. I set up artificial markets to derive closed-form solutions for my life-cycle problem and transform the resulting c
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Inheritance of convexity for the $$\mathcal {P}_{\min }$$ P min -restricted game Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-09-16 A. Skoda
We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the sub-components corresponding to a minimum partition. This minimum partition \(\mathcal {P}_{\min }\) is induced by the deletion of the minimum weight edges. We provide a characterization of the graphs satisfying
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The residual time approach for ( Q , r ) model under perishability, general lead times, and lost sales Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-07-31 Yonit Barron, Opher Baron
We consider a (Q, r) perishable inventory system with state-dependent compound Poisson demands with a random batch size, general lead times, exponential shelf times, and lost sales. We assume \(r
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Decentralization and mutual liability rules Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-07-30 Martijn Ketelaars, Peter Borm, Marieke Quant
This paper builds on the recent work of Groote Schaarsberg et al. (Math Methods Oper Res 87(3):383–409, 2018) on mutual liability problems. In essence, a mutual liability problem comprises a financial network in which agents may have both monetary individual assets and mutual liabilities. Here, mutual liabilities reflect rightful monetary obligations from past bilateral transactions. To settle these
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On the facet defining inequalities of the mixed-integer bilinear covering set Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-07-27 Hamidur Rahman, Ashutosh Mahajan
We study the facet defining inequalities of the convex hull of a mixed-integer bilinear covering arising in trim-loss (or cutting stock) problem under the framework of disjunctive cuts. We show that all of them can be derived using a disjunctive procedure. Some of these are split cuts of rank one for a convex mixed-integer relaxation of the covering set, while others have rank at least two. For certain
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A conservative index heuristic for routing problems with multiple heterogeneous service facilities Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-07-22 Rob Shone, Vincent A. Knight, Paul R. Harper
We consider a queueing system with N heterogeneous service facilities, in which admission and routing decisions are made when customers arrive and the objective is to maximize long-run average net rewards. For this type of problem, it is well-known that structural properties of optimal policies are difficult to prove in general and dynamic programming methods are computationally infeasible unless N
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On computation of optimal strategies in oligopolistic markets respecting the cost of change Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-07-21 Jiří V. Outrata, Jan Valdman
The paper deals with a class of parameterized equilibrium problems, where the objectives of the players do possess nonsmooth terms. The respective Nash equilibria can be characterized via a parameter-dependent variational inequality of the second kind, whose Lipschitzian stability, under appropriate conditions, is established. This theory is then applied to evolution of an oligopolistic market in which
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Optimal dividends and capital injection under dividend restrictions Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-07-16 Kristoffer Lindensjö, Filip Lindskog
We study a singular stochastic control problem faced by the owner of an insurance company that dynamically pays dividends and raises capital in the presence of the restriction that the surplus process must be above a given dividend payout barrier in order for dividend payments to be allowed. Bankruptcy occurs if the surplus process becomes negative and there are proportional costs for capital injection
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Robust best choice problem Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-07-09 Lazar Obradović
We consider a robust version of the full information best choice problem: there is model uncertainty, represented by a set of priors, about the measure driving the observed process. We propose a general construction of the set of priors that we use to solve the problem in the setting of Riedel (Econometrica 77(3):857–908, 2009). As in the classical case, it is optimal to stop if the current observation
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Solutions for subset sum problems with special digraph constraints Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-07-03 Frank Gurski, Dominique Komander, Carolin Rehs
The subset sum problem is one of the simplest and most fundamental NP-hard problems in combinatorial optimization. We consider two extensions of this problem: The subset sum problem with digraph constraint (SSG) and subset sum problem with weak digraph constraint (SSGW). In both problems there is given a digraph with sizes assigned to the vertices. Within SSG we want to find a subset of vertices whose
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Discrete-time control with non-constant discount factor Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-06-27 Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau
This paper deals with discrete-time Markov decision processes (MDPs) with Borel state and action spaces, and total expected discounted cost optimality criterion. We assume that the discount factor is not constant: it may depend on the state and action; moreover, it can even take the extreme values zero or one. We propose sufficient conditions on the data of the model ensuring the existence of optimal
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An augmented Lagrangian filter method Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-06-24 Sven Leyffer, Charlie Vanaret
We introduce a filter mechanism to enforce convergence for augmented Lagrangian methods for nonlinear programming. In contrast to traditional augmented Lagrangian methods, our approach does not require the use of forcing sequences that drive the first-order error to zero. Instead, we employ a filter to drive the optimality measures to zero. Our algorithm is flexible in the sense that it allows for
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A long-time asymptotic solution to the g-renewal equation for underlying distributions with nondecreasing hazard functions Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-06-13 Serguei Maximov, Consuelo de J. Cortes-Penagos
The Kijima’s type 1 maintenance model, representing the general renewal process, is one of the most important in the reliability theory. The g-renewal equation is central in Kijima’s theory and it is a Volterra integral equation of the second kind. Although these equations are well-studied, a closed-form solution to the g-renewal equation has not yet been obtained. Despite the fact that several semi-empirical
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Optimising dividends and consumption under an exponential CIR as a discount factor Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-06-03 Julia Eisenberg, Yuliya Mishura
We consider an economic agent (a household or an insurance company) modelling its surplus process by a deterministic process or by a Brownian motion with drift. The goal is to maximise the expected discounted spending/dividend payments under a discounting factor given by an exponential CIR process. In the deterministic case, we are able to find explicit expressions for the optimal strategy and the
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Min max min robust (relative) regret combinatorial optimization Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-05-19 Alejandro Crema
We consider combinatorial optimization problems with uncertainty in the cost vector. Recently, a novel approach was developed to deal with such uncertainties: instead of a single one robust solution, obtained by solving a min max problem, the authors consider a set of solutions obtained by solving a min max min problem. In this new approach, the set of solutions is computed once and we can choose the
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A new nonmonotone smoothing Newton method for the symmetric cone complementarity problem with the Cartesian $$P_0$$P0 -property Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-04-17 Xiangjing Liu, Sanyang Liu
We present a new smoothing Newton method for the symmetric cone complementarity problem with the Cartesian \(P_0\)-property. The new method is based on a new smoothing function and a nonmonotone line search which contains a monotone line search as a special case. It is proved that the new method is globally and locally superlinearly/quadratically convergent under mild conditions. Preliminary numerical
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On weak conjugacy, augmented Lagrangians and duality in nonconvex optimization Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-03-19 Gulcin Dinc Yalcin, Refail Kasimbeyli
In this paper, zero duality gap conditions in nonconvex optimization are investigated. It is considered that dual problems can be constructed with respect to the weak conjugate functions, and/or directly by using an augmented Lagrangian formulation. Both of these approaches and the related strong duality theorems are studied and compared in this paper. By using the weak conjugate functions approach
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First-order sensitivity of the optimal value in a Markov decision model with respect to deviations in the transition probability function Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-03-02 Patrick Kern, Axel Simroth, Henryk Zähle
Markov decision models (MDM) used in practical applications are most often less complex than the underlying ‘true’ MDM. The reduction of model complexity is performed for several reasons. However, it is obviously of interest to know what kind of model reduction is reasonable (in regard to the optimal value) and what kind is not. In this article we propose a way how to address this question. We introduce
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Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-02-12 Valentin Hartmann, Dominic Schuhmacher
We consider the problem of finding an optimal transport plan between an absolutely continuous measure and a finitely supported measure of the same total mass when the transport cost is the unsquared Euclidean distance. We may think of this problem as closest distance allocation of some resource continuously distributed over Euclidean space to a finite number of processing sites with capacity constraints
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On the rectangular knapsack problem: approximation of a specific quadratic knapsack problem Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-02-12 Britta Schulze, Michael Stiglmayr, Luís Paquete, Carlos M. Fonseca, David Willems, Stefan Ruzika
In this article, we introduce the rectangular knapsack problem as a special case of the quadratic knapsack problem consisting in the maximization of the product of two separate knapsack profits subject to a cardinality constraint. We propose a polynomial time algorithm for this problem that provides a constant approximation ratio of 4.5. Our experimental results on a large number of artificially generated
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A pricing problem with unknown arrival rate and price sensitivity Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-02-11 Athanassios N. Avramidis
We study a pricing problem with finite inventory and semi-parametric demand uncertainty. Demand is a price-dependent Poisson process whose mean is the product of buyers’ arrival rate, which is a constant \(\lambda \), and buyers’ purchase probability \(q(p)\), where p is the price. The seller observes arrivals and sales, and knows neither \(\lambda \) nor \(q\). Based on a non-parametric maximum-likelihood
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Continuity and monotonicity of solutions to a greedy maximization problem Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-02-10 Łukasz Kruk
Motivated by an application to resource sharing network modelling, we consider a problem of greedy maximization (i.e., maximization of the consecutive minima) of a vector in \({\mathbb {R}}^n\), with the admissible set indexed by the time parameter. The structure of the constraints depends on the underlying network topology. We investigate continuity and monotonicity of the resulting maximizers with
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Statistical properties of estimators for the log-optimal portfolio Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-01-25 Gabriel Frahm
The best constant re-balanced portfolio represents the standard estimator for the log-optimal portfolio. It is shown that a quadratic approximation of log-returns works very well on a daily basis and a mean-variance estimator is proposed as an alternative to the best constant re-balanced portfolio. It can easily be computed and the numerical algorithm is very fast even if the number of dimensions is
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Qualitative robustness of set-valued value-at-risk Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-02-17 Giovanni Paolo Crespi; Elisa Mastrogiacomo
Risk measures are defined as functionals of the portfolio loss distribution, thus implicitly assuming the knowledge of such a distribution. However, in practical applications, the need for estimation arises and with it the need to study the effects of mis-specification errors, as well as estimation errors on the final conclusion. In this paper we focus on the qualitative robustness of a sequence of
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Some results on optimal stopping under phase-type distributed implementation delay Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-01-08 Jukka Lempa
We study optimal stopping of strong Markov processes under random implementation delay. By random implementation delay we mean the following: the payoff is not realised immediately when the process is stopped but rather after a random waiting period. The distribution of the random waiting period is assumed to be phase-type. We prove first a general result on the solvability of the problem. Then we
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An asymptotically optimal strategy for constrained multi-armed bandit problems Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-01-02 Hyeong Soo Chang
This note considers the model of “constrained multi-armed bandit” (CMAB) that generalizes that of the classical stochastic MAB by adding a feasibility constraint for each action. The feasibility is in fact another (conflicting) objective that should be kept in order for a playing-strategy to achieve the optimality of the main objective. While the stochastic MAB model is a special case of the Markov
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An inexact primal-dual algorithm for semi-infinite programming Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2020-01-01 Bo Wei; William B. Haskell; Sixiang Zhao
This paper considers an inexact primal-dual algorithm for semi-infinite programming (SIP) for which it provides general error bounds. We create a new prox function for nonnegative measures for the dual update, and it turns out to be a generalization of the Kullback-Leibler divergence. We show that, with a tolerance for small errors (approximation and regularization error), this algorithm achieves an
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A finite horizon optimal switching problem with memory and application to controlled SDDEs Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-12-27 Magnus Perninge
We consider an optimal switching problem where the terminal reward depends on the entire control trajectory. We show existence of an optimal control by applying a probabilistic technique based on the concept of Snell envelopes. We then apply this result to solve an impulse control problem for stochastic delay differential equations driven by a Brownian motion and an independent compound Poisson process
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Counting and enumerating independent sets with applications to combinatorial optimization problems Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-12-17 Frank Gurski; Carolin Rehs
Counting and enumerating maximal and maximum independent sets are well-studied problems in graph theory. In this paper we introduce methods to count and enumerate maximal/maximum independent sets in threshold graphs and k-threshold graphs and improve former results for these problems. The results can be applied to combinatorial optimization problems, and in particular to different variations of the
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The stability and extended well-posedness of the solution sets for set optimization problems via the Painlevé–Kuratowski convergence Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-12-16 Yu Han; Kai Zhang; Nan-jing Huang
In this paper, we obtain the Painlevé–Kuratowski upper convergence and the Painlevé–Kuratowski lower convergence of the approximate solution sets for set optimization problems with the continuity and convexity of objective mappings. Moreover, we discuss the extended well-posedness and the weak extended well-posedness for set optimization problems under some mild conditions. We also give some examples
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Optimal control of an objective functional with non-linearity between the conditional expectations: solutions to a class of time-inconsistent portfolio problems Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-12-12 Esben Kryger; Maj-Britt Nordfang; Mogens Steffensen
We present a modified verification theorem for the equilibrium control of a general class of portfolio problems. The general class of portfolio problems studied in this paper, is characterized by an objective where the investor seeks to maximize a functional of two conditional expectations of terminal wealth. The objective functional is allowed to be non-linear in the conditional expectations, and
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Convergence properties of a class of exact penalty methods for semi-infinite optimization problems Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-12-05 Jiachen Ju; Qian Liu
In this paper, a new class of unified penalty functions are derived for the semi-infinite optimization problems, which include many penalty functions as special cases. They are proved to be exact in the sense that under Mangasarian–Fromovitz constraint qualification conditions, a local solution of penalty problem is a corresponding local solution of original problem when the penalty parameter is sufficiently
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Discounted approximations in risk-sensitive average Markov cost chains with finite state space Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-12-05 Rubén Blancas-Rivera; Rolando Cavazos-Cadena; Hugo Cruz-Suárez
This work concerns with Markov chains on a finite state space. It is supposed that a state-dependent cost is associated with each transition, and that the evolution of the system is watched by an agent with positive and constant risk-sensitivity. For a general transition matrix, the problem of approximating the risk-sensitive average criterion in terms of the risk-sensitive discounted index is studied
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The Douglas–Rachford algorithm for convex and nonconvex feasibility problems Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-11-26 Francisco J. Aragón Artacho; Rubén Campoy; Matthew K. Tam
The Douglas–Rachford algorithm is an optimization method that can be used for solving feasibility problems. To apply the method, it is necessary that the problem at hand is prescribed in terms of constraint sets having efficiently computable nearest points. Although the convergence of the algorithm is guaranteed in the convex setting, the scheme has demonstrated to be a successful heuristic for solving
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A McKean–Vlasov approach to distributed electricity generation development Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-11-26 René Aïd; Matteo Basei; Huyên Pham
This paper analyses the interaction between centralised carbon emissive technologies and distributed intermittent non-emissive technologies. In our model, there is a representative consumer who can satisfy her electricity demand by investing in distributed generation (solar panels) and by buying power from a centralised firm at a price the firm sets. Distributed generation is intermittent and induces
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A note on the combination of equilibrium problems Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-11-12 Nguyen Thi Thanh Ha; Tran Thi Huyen Thanh; Nguyen Ngoc Hai; Hy Duc Manh; Bui Van Dinh
We show that the solution set of a strictly convex combination of equilibrium problems is not necessarily contained in the corresponding intersection of solution sets of equilibrium problems even if the bifunctions defining the equilibrium problems are continuous and monotone. As a consequence, we show that some results given in some recent papers are not always true. Therefore different numerical
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A class of linear quadratic dynamic optimization problems with state dependent constraints Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-11-06 Rajani Singh; Agnieszka Wiszniewska-Matyszkiel
In this paper, we analyse a wide class of discrete time one-dimensional dynamic optimization problems—with strictly concave current payoffs and linear state dependent constraints on the control parameter as well as non-negativity constraint on the state variable and control. This model suits well economic problems like extraction of a renewable resource (e.g. a fishery or forest harvesting). The class
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Random optimization on random sets Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-10-18 Emmanuel Lepinette
Random sets and random preorders naturally appear in financial market modeling with transaction costs. In this paper, we introduce and study a concept of essential minimum for a family of vector-valued random variables, as a set of minimal elements with respect to some random preorder. We provide some conditions under which the essential minimum is not empty and we present two applications in optimisation
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A simple construction of complete single-peaked domains by recursive tiling Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-10-10 Ping Zhan
Single-peakedness was introduced by Black (J Political Econ 56:23–34, 1948) as a sufficient condition to overcome Condorcet paradox. Since then it has been attracting interest from researchers in various fields. In this paper, we propose a simple recursive procedure of constructing complete single-peaked domains of tiling type explicitly for any finite alternative sets, by combining two results published
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Virtual allocation policies for many-server queues with abandonment Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-10-08 Zhenghua Long; Jiheng Zhang
We study a multiclass many-server queueing system with renewal arrivals and generally distributed service and patience times under a nonpreemptive allocation policy. The status of the system is described by a pair of measure-valued processes to track the residual service and patience times of customers in each class. We establish fluid approximations and study the long-term behavior of the fluid model
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Martingale optimal transport in the discrete case via simple linear programming techniques Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-10-08 Nicole Bäuerle; Daniel Schmithals
We consider the problem of finding consistent upper price bounds and super replication strategies for exotic options, given the observation of call prices in the market. This field of research is called model-independent finance and has been introduced by Hobson (Finance Stoch 2(4):329–347, 1998). Here we use the link to mass transport problems. In contrast to existing literature we assume that the
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Order and exit decisions under non-increasing price curves for products with short life cycles Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-09-17 J. B. G. Frenk; Canan Pehlivan; Semih O. Sezer
We consider a supplier selling a product with a relatively short life cycle and following a non-increasing price curve. Because of the short cycle, there is a single procurement opportunity at the beginning of the cycle. The objective of the supplier is to determine the initial order quantity and the time to remove the product from the market in order to maximize her profits. We study this problem
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An optimal stopping approach for the end-of-life inventory problem Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-09-11 J. B. G. Frenk; Sonya Javadi; Semih O. Sezer
We consider the end-of-life inventory problem for the supplier of a product in its final phase of the service life cycle. This phase starts when the production of the items stops and continues until the warranty of the last sold item expires. At the beginning of this phase the supplier places a final order for spare parts to serve customers coming with defective items. At any time during the final
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A continuous selection for optimal portfolios under convex risk measures does not always exist Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-09-10 Michel Baes; Cosimo Munari
Risk control is one of the crucial problems in finance. One of the most common ways to mitigate risk of an investor’s financial position is to set up a portfolio of hedging securities whose aim is to absorb unexpected losses and thus provide the investor with an acceptable level of security. In this respect, it is clear that investors will try to reach acceptability at the lowest possible cost. Mathematically
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The polyhedral projection problem Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-08-29 Benjamin Weißing
We revisit the polyhedral projection problem. This problem has many applications, among them certain problems in global optimisation, polyhedral calculus, problems encountered in information theory and financial mathematics. In particular, it has been shown recently that polyhedral projection problems are equivalent to vector linear programmes (which contain multiple objective linear programmes as
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Ekeland’s variational principle with weighted set order relations Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-08-26 Qamrul Hasan Ansari; Andreas H Hamel; Pradeep Kumar Sharma
The main results of the paper are a minimal element theorem and an Ekeland-type variational principle for set-valued maps whose values are compared by means of a weighted set order relation. This relation is a mixture of a lower and an upper set relation which form the building block for modern approaches to set-valued optimization. The proofs rely on nonlinear scalarization functions which admit to
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Optimal control of electricity input given an uncertain demand Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-08-14 Simone Göttlich; Ralf Korn; Kerstin Lux
We consider the problem of determining an optimal strategy for electricity injection that faces an uncertain power demand stream. This demand stream is modeled via an Ornstein–Uhlenbeck process with an additional jump component, whereas the power flow is represented by the linear transport equation. We analytically determine the optimal amount of power supply for different levels of available information
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Multi-criteria decision making via multivariate quantiles Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-08-02 Daniel Kostner
A novel approach for solving a multiple judge, multiple criteria decision making (MCDM) problem is proposed. The presence of multiple criteria leads to a non-total order relation. The ranking of the alternatives in such a framework is done by reinterpreting the MCDM problem as a multivariate statistics one and by applying the concepts in Hamel and Kostner (J Multivar Anal 167:97–113, 2018). A function
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A new concept of slope for set-valued maps and applications in set optimization studied with Kuroiwa’s set approach Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-07-26 Truong Xuan Duc Ha
In this paper, we introduce a new concept of slope for a set-valued map using a scalarizing function defined with the help of the Hiriart-Urruty signed distance function. It turns out that this slope possesses most properties of the strong slope of a scalar-valued function. We present some applications in set optimization studied with Kuroiwa’s set approach. Namely, we obtain criteria for error bounds
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Accelerated first-order methods for large-scale convex optimization: nearly optimal complexity under strong convexity Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-06-26 Masoud Ahookhosh
We introduce four accelerated (sub)gradient algorithms (ASGA) for solving several classes of convex optimization problems. More specifically, we propose two estimation sequences majorizing the objective function and develop two iterative schemes for each of them. In both cases, the first scheme requires the smoothness parameter and a Hölder constant, while the second scheme is parameter-free (except
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The blockwise coordinate descent method for integer programs Math. Meth. Oper. Res. (IF 1.0) Pub Date : 2019-06-15 Sven Jäger; Anita Schöbel
Blockwise coordinate descent methods have a long tradition in continuous optimization and are also frequently used in discrete optimization under various names. New interest in blockwise coordinate descent methods arises for improving sequential solutions for problems which consist of several planning stages. In this paper we systematically formulate and analyze the blockwise coordinate descent method