We study combinatorial structures in large-scale mixed-integer (nonlinear) programming problems arising in gas network optimization. We propose a preprocessing strategy exploiting the observation that a large part of the combinatorial complexity arises in certain subnetworks. Our approach analyzes these subnetworks and the combinatorial structure of the flows within these subnetworks in order to provide

A Correction to this paper has been published: 10.1007/s00186-015-0499-8

Pairs trading is a typical example of a convergence trading strategy. Investors buy relatively under-priced assets simultaneously, and sell relatively over-priced assets to exploit temporary mispricing. This study examines optimal pairs trading strategies under symmetric and non-symmetric trading constraints. Under the assumption that the price spread of a pair of correlated securities follows a mean-reverting

In this article, we enhance the study of stochastic comparisons and ageing properties of residual lifetime mixture models. To this aim, first we perform stochastic comparisons of two different mixture models under likelihood ratio, hazard rate, mean residual life and variance residual life orders having different baseline distributions as well as two different mixing distributions. Then, we develop

In this paper an order on the set of embedded coalitions is studied in detail. This allows us to define new notions of superaddivity and convexity of games in partition function form which are compared to other proposals in the literature. The main results are two characterizations of convexity. The first one uses non-decreasing contributions to coalitions of increasing size and can thus be considered

In this paper, we consider an n-player non-cooperative game where the random payoff function of each player is defined by its expected value and her strategy set is defined by a joint chance constraint. The random constraint vectors are independent. We consider the case when the probability distribution of each random constraint vector belongs to a subset of elliptical distributions as well as the

We study the minimization of a spectral risk measure of the total discounted cost generated by a Markov Decision Process (MDP) over a finite or infinite planning horizon. The MDP is assumed to have Borel state and action spaces and the cost function may be unbounded above. The optimization problem is split into two minimization problems using an infimum representation for spectral risk measures. We

We study price optimization of perishable inventory over multiple, consecutive selling seasons in the presence of demand uncertainty. Each selling season consists of a finite number of discrete time periods, and demand per time period is Bernoulli distributed with price-dependent parameter. The set of feasible prices is finite, and the expected demand corresponding to each price is unknown to the seller

In this paper, we propose three new axiomatizations of the Owen value, similar as the axiomatizations of the Shapley value of Chun (Int J Game Theory 20(2):183–190, 1991), van den Brink (Int J Game Theory 30(3):309–319, 2002), and Manuel et al. (Math Methods Oper Res 77:1–14, 2013), respectively. Firstly, we show that the additivity and null player property in Owen’s (in: Henn and Moeschlin (eds) Mathematical

We study cooperative solutions for differential games where players consume a common property resource. Players are asymmetric, in the sense that they have different preferences and, in particular, different time preferences. We propose a new time-consistent dynamic bargaining procedure for this class of games. This solution concept, which is defined as the time-consistent dynamic bargaining (TCB)

In this article, we introduce the Maximum Diversity Assortment Selection Problem (MDASP), which is a generalization of the two-dimensional Knapsack Problem (2D-KP). Given a set of rectangles and a rectangular container, the goal of 2D-KP is to determine a subset of rectangles that can be placed in the container without overlapping, i.e., a feasible assortment, such that a maximum area is covered. MDASP

We consider relative or subjective optimization problems where the goal function and feasible set are dependent on the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence finding their solutions may be rather difficult. We describe a rather general class of relative optimization problems in metric spaces, which in addition depend on

Many interactions from linear production problems, financial markets, or sequencing problems are modeled by cooperative games where payoffs to a coalition of players is a random variable. For this class of cooperative games, we introduce a two-stage value as an ex-ante agreement among players. Players are first promised their prior Shapley shares which are exactly their respective shares by the Shapley

We consider a single-period portfolio selection problem for an investor, maximizing the expected ratio of the portfolio utility to the utility of a best asset taken in hindsight. The decision rules are based on the history of stock returns with unknown distribution. Assuming that the utility function is Lipschitz or Hölder continuous (the concavity is not required), we obtain high probability utility

In the setting of normed spaces ordered by a convex cone not necessarily solid, we use six set scalarization functions, which are extensions of the oriented distance of Hiriart-Urruty, and we discuss convexity and continuity properties of their composition with two set-valued maps. Furthermore, as an application, we derive a multiplier rule for weak minimal solutions of a convex set optimization problem

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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