This paper presents a new trust region method for multiobjective heterogeneous optimization problems. One of the objective functions is an expensive black-box function, for example given by a time-consuming simulation. For this function derivative information cannot be used and the computation of function values involves high computational effort. The other objective functions are given analytically … Read more
A new branch-and-bound based algorithm for smooth nonconvex multiobjective optimization problems with convex constraints is presented. The algorithm computes an $(\varepsilon,\delta)$-approximation of all globally optimal solutions. We introduce the algorithm which uses selection rules, discarding and termination tests. The discarding tests are the most important aspect, as they examine in different ways whether a box … Read more
This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest path problem in an auxiliary network. We design tools and techniques for exploiting the network model in … Read more
Many problems in real life have more than one decision criterion, referred to as multi-objective optimization (MOO) problems, and the objective functions of these problems are conflicting in most cases. Hence, finding non-dominated solutions is very critical for decision making process. Tri-objective mixed-integer linear programs (TOMILP) are an important subclass of MOOs that are applicable … Read more
Set optimization with the set approach has recently gained increasing interest due to its practical relevance. In this problem class one studies optimization problems with a set-valued objective map and defines optimality based on a direct comparison of the images of the objective function, which are sets here. Meanwhile, in the literature a wide range … Read more
In this paper, we present an algorithm for solving stochastic minimax dynamic programmes where state and action sets are convex and compact. A feature of the formulations studied is the simultaneous non-rectangularity of both `min’ and `max’ feasibility sets. We begin by presenting convex programming upper and lower bound representations of saddle functions — extending … Read more
Generalized Nash Equilibrium Problems (GNEPs) are a generalization of the classic Nash Equilibrium Problems (NEPs), where each player’s strategy set depends on the choices of the other players. In this work we study constraint qualifications and optimality conditions tailored for GNEPs and we discuss their relations and implications for global convergence of algorithms. Surprisingly, differently … Read more
We develop a new class of approximate linear programs (ALPs) that project the high-dimensional value function of dynamic programs onto a class of basis functions, each defined as a network that represents aggregrations over the state space. The resulting ALP is a minimum-cost flow problem over an extended variable space that synchronizes flows across multiple … Read more
It is shown how to use the performance and data profile benchmarking tools to improve algorithms’ performance. An illustration for the BFO derivative-free optimizer suggests that the obtained gains are potentially significant. CitationACM Transactions on Mathematical Software, 45:2 (2019), Article 20.ArticleDownload View PDF
We consider an n-player non-cooperative game with random payoffs and continuous strategy set for each player. The random payoffs of each player are defined using a finite dimensional random vector. We formulate this problem as a chance-constrained game by defining the payoff function of each player using a chance constraint. We first consider the case … Read more