Optimal configurations for modular systems at the example of crane bridges

The aim of this paper is to optimize modular systems which cover the construction of products that can be assembled on a modular basis. Increasing the number of different variants of individual components on the one hand decreases the cost of oversizing the assembled product, while on the other hand the cost for maintaining the … Read more

On the weakest constraint qualification for strong local minimizers

The strong local minimality of feasible points of nonlinear optimization problems is known to possess a characterization by a strengthened version of the Karush-Kuhn-Tucker conditions, as long as the Mangasarian-Fromovitz constraint qualification holds. This strengthened condition is not easy to check algorithmically since it involves the topological interior of some set. In this paper we … Read more

A branch-and-prune algorithm for discrete Nash equilibrium problems

We present a branch-and-prune procedure for discrete Nash equilibrium problems with a convex description of each player’s strategy set. The derived pruning criterion does not require player convexity, but only strict convexity of some player’s objective function in a single variable. If satisfied, it prunes choices for this variable by stating activity of certain constraints. … Read more

Semi-infinite models for equilibrium selection

In their seminal work `A General Theory of Equilibrium Selection in Games’ (The MIT Press, 1988) Harsanyi and Selten introduce the notion of payoff dominance to explain how players select some solution of a Nash equilibrium problem from a set of nonunique equilibria. We formulate this concept for generalized Nash equilibrium problems, relax payoff dominance … Read more

A deterministic solver for multiobjective mixed-integer convex and nonconvex optimization

This paper proposes a general framework for solving multiobjective nonconvex optimization problems, i.e., optimization problems in which multiple objective functions have to be optimized simultaneously. Thereby, the nonconvexity might come from the objective or constraint functions, or from integrality conditions for some of the variables. In particular, multiobjective mixed-integer convex and nonconvex optimization problems are … Read more

Feasible rounding approaches and diving strategies in branch-and-bound methods for mixed-integer optimization

In this paper, we study the behavior of feasible rounding approaches for mixed-integer linear and nonlinear optimization problems (MILP and MINLP, respectively) when integrated into tree search of branch-and-bound. Our research addresses two important aspects. First, we develop insights into how an (enlarged) inner parallel set, which is the main component for feasible rounding approaches, … Read more

Limit sets in global multiobjective optimization

Inspired by the recently introduced branch-and-bound method for continuous multiobjective optimization problems from G. Eichfelder, P. Kirst, L. Meng, O. Stein, A general branch-and-bound framework for continuous global multiobjective optimization, Journal of Global Optimization, 80 (2021) 195-227, we study for a general class of branch-and-bound methods in which sense the generated terminal enclosure and the … Read more

Recent Advances in Nonconvex Semi-infinite Programming: Applications and Algorithms

The goal of this literature review is to give an update on the recent developments for semi-infinite programs (SIPs), approximately over the last 20 years. An overview of the different solution approaches and the existing algorithms is given. We focus on deterministic algorithms for SIPs which do not make any convexity assumptions. In particular, we … Read more

Feasible rounding approaches for equality constrained mixed-integer optimization problems

A feasible rounding approach is a novel technique to compute good feasible points for mixed-integer optimization problems. The central idea of this approach is the construction of a continuously described inner parallel set for which any rounding of any of its elements is feasible in the original mixed-integer problem. It is known that this approach … Read more

A general branch-and-bound framework for continuous global multiobjective optimization

Current generalizations of the central ideas of single-objective branch-and-bound to the multiobjective setting do not seem to follow their train of thought all the way. The present paper complements the various suggestions for generalizations of partial lower bounds and of overall upper bounds by general constructions for overall lower bounds from partial lower bounds, and … Read more