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

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

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

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

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

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

In the framework of normed spaces ordered by a convex cone not necessarily solid, we consider two set scalarization functions of type sup-inf, which are extensions of the oriented distance of Hiriart-Urruty. We investigate some of their properties and, moreover, we use these functions to characterize the lower and upper set less preorders of Kuroiwa and the strict lower and strict upper set relations

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

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

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

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

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

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

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

We apply the well-known Condorcet criterion from voting theory outside of its classical framework and link it with spanning trees of an undirected graph. In situations in which a network, represented by a spanning tree of an undirected graph, needs to be installed, decision-makers typically do not agree on the network to be implemented. Instead, each of these decision-makers has her own ideal conception

We consider the Erlang A model, or [Formula: see text] queue, with Poisson arrivals, exponential service times, and m parallel servers, and the property that waiting customers abandon the queue after an exponential time. The queue length process is in this case a birth-death process, for which we obtain explicit expressions for the Laplace transforms of the time-dependent distribution and the first

This paper introduces mutual liability problems, as a generalization of bankruptcy problems, where every agent not only owns a certain amount of cash money, but also has outstanding claims and debts towards the other agents. Assuming that the agents want to cash their claims, we will analyze mutual liability rules which prescribe how the total available amount of cash should be allocated among the

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