Two-stage distributionally robust noncooperative games: Existence of Nash equilibria and its application to Cournot-Nash competition

Two-stage distributionally robust stochastic noncooperative games with continuous decision variables are studied. In such games, each player solves a two-stage distributionally robust optimization problem depending on the decisions of the other players. Existing studies in this area have been limited with strict assumptions, such as linear decision rules, and supposed that each player solves a … Read more

Computing Tchebychev weight space decomposition for multiobjective discrete optimization problems

Multiobjective discrete optimization (MODO) techniques, including weight space decomposition, have received increasing attention in the last decade. The primary weight space decomposition technique in the literature is defined for the weighted sum utility function, through which sets of weights are assigned to a subset of the nondominated set. Recent work has begun to study the … Read more

Multilinear formulations for computing Nash equilibrium of multi-player matrix games

We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player strategic-form games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program finds a Nash equilibrium faster than any of the methods we compare it to, including the quantal response equilibrium method, which is recommended … Read more

Computing an enclosure for multiobjective mixed-integer nonconvex optimization problems using piecewise linear relaxations

In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer problems without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonconvexity of the original problem. The method chooses adaptively which level of relaxation is … Read more

Multi-Echelon Inventory Management for a Non-Stationary Capacitated Distribution Network

We present an inventory management solution for a non-stationary capacitated multi-echelon distribution network involving thousands of products. Assuming backlogged sales, we revisit and leverage the seminal multi-echelon inventory management results in the literature to establish the structural properties of the problem, and derive an efficient and practical solution method. In particular, we describe how the … Read more

Using Neural Networks to Solve Linear Bilevel Problems with Unknown Lower Level

Bilevel problems are used to model the interaction between two decision makers in which the lower-level problem, the so-called follower’s problem, appears as a constraint in the upper-level problem of the so-called leader. One issue in many practical situations is that the follower’s problem is not explicitly known by the leader. For such bilevel problems … Read more

A unified scheme for scalarization in set optimization

In this work, we propose a new scheme for scalarization in set optimization studied with the Kuroiwa set appoach. First, we define an abstract scalarizing function possessing properties such as global Lipschizity, sublinearity, cone monotonicity, cone representation property, cone interior representation property and uniform positivity. Next, we use this function to define the so called … Read more

Convergence of Trajectory Following Dynamic Programming algorithms for multistage stochastic problems without finite support assumptions

We introduce a class of algorithms, called Trajectory Following Dynamic Programming (TFDP) algorithms, that iteratively refines approximation of cost-to-go functions of multistage stochastic problems with independent random variables. This framework encompasses most variants of the Stochastic Dual Dynamic Programming algorithm. Leveraging a Lipschitz assumption on the expected cost-to-go functions, we provide a new convergence and … Read more

Solving large-scale unit-commitment problems using dual dynamic programming and open-source solvers

The astonishing dimensions and complexity of power systems render them impossible to be managed without the help of cutting-edge software. Due to a lack of scalable, reliable and well documented free and open-source solutions, system operators, regulators, and government agencies often rely on proprietary software to provide them information that ultimately will be used to … Read more