Addressing Hierarchical Jointly-Convex Generalized Nash Equilibrium Problems with Nonsmooth Payoffs

We consider a Generalized Nash Equilibrium Problem whose joint feasible region is implicitly defined as the solution set of another Nash game. This structure arises e.g. in multi-portfolio selection contexts, whenever agents interact at different hierarchical levels. We consider nonsmooth terms in all players’ objectives, to promote, for example, sparsity in the solution. Under standard … Read more

Computing an approximation of the nondominated set of multi-objective mixed-integer nonlinear optimization problems

In practical applications, one often has not only one, but several objectives that need to be optimized simultaneously. What is more, modeling such real world problems usually involves using both, continuous and integer variables. This then results in multi-objective mixed-integer optimization problems, which are in focus of this paper. We present an approximation concept, called … Read more

From Optimization to Control: Quasi Policy Iteration

Recent control algorithms for Markov decision processes (MDPs) have been designed using an implicit analogy with well-established optimization algorithms. In this paper, we make this analogy explicit across four problem classes with a unified solution characterization. This novel framework, in turn, allows for a systematic transformation of algorithms from one domain to the other. In … Read more

Budget Constrained Maximization of “Cobb-Douglas with Linear Components” Utility Function

In what follows, we provide the demand analysis associated with budget constrained linear utility maximization for each of several categories of goods, with the marginal rate of consumption expenditure-as a share of wealth- being a positive constant less than one. The marginal rate of consumption expenditure is endogenously determined, by a budget constrained “Cobb-Douglas with … Read more

Neural Approximate Dynamic Programming for the Ultra-fast Order Dispatching Problem

Same-Day Delivery (SDD) services aim to maximize the fulfillment of online orders while minimizing delivery delays but are beset by operational uncertainties such as those in order volumes and courier planning. Our work aims to enhance the operational efficiency of SDD by focusing on the ultra-fast Order Dispatching Problem (ODP), which involves matching and dispatching … Read more

A Generic Hybrid Genetic Algorithm-based Framework for Solving Various Classes of Arc Routing Problems

Arc routing problems are combinatorial optimization problems that have many real-world applications, such as mail delivery, snow plowing, and waste collection. Various variants of this problem are available, as well as algorithms intended to solve them heuristically or exactly. Presented here is a generic algorithmic framework that can be applied to a variety of arc … Read more

Combining Precision Boosting with LP Iterative Refinement for Exact Linear Optimization

This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of precision boosting inside an LP iterative refinement loop, the combined algorithm is able to leverage the strengths of both methods: … Read more

Price of Anarchy in Paving Matroid Congestion Games

Congestion games allow to model competitive resource sharing in various distributed systems. Pure Nash equilibria, that are stable outcomes of a game, could be far from being socially optimal. Our goal is to identify combinatorial structures that limit the inefficiency of equilibria. This question has been mainly investigated for congestion games defined over networks. Instead, … Read more

Strategy Investments in Matrix Games

We propose an extension of matrix games where the row player may select rows and remove columns, subject to a budget constraint. We present an exact mixed-integer linear programming (MILP) formulation for the problem, provide analytical results concerning its solution, and discuss applications in the security domain. Our computational experiments show heuristic approaches on average … Read more

Bi-level multi-criteria optimization to include linear energy transfer into proton treatment planning

In proton therapy treatment planning, the aim is to ensure tumor control while sparing the various surrounding risk structures. The biological effect of the irradiation depends on both physical dose and linear energy transfer (LET). In order to include LET alongside physical dose in plan creation, we propose to formulate the proton treatment planning problem … Read more