Asynchronous parallel generating set search for linearly-constrained optimization

Generating set search (GSS) is a family of direct search methods that encompasses generalized pattern search and related methods. We describe an algorithm for asynchronous linearly-constrained GSS, which has some complexities that make it different from both the asynchronous bound-constrained case as well as the synchronous linearly-constrained case. The algorithm has been implemented in the … Read more

Copositivity cuts for improving SDP bounds on the clique number

Adding cuts based on copositive matrices, we propose to improve Lovász’ bound on the clique number and its tightening introduced by McEliece, Rodemich, Rumsey, and Schrijver. Candidates for cheap and efficient copositivity cuts of this type are obtained from graphs with known clique number. The cost of previously established semidefinite programming bound hierarchies rapidly increases … Read more

Polytopes and Arrangements : Diameter and Curvature

We introduce a continuous analogue of the Hirsch conjecture and a discrete analogue of the result of Dedieu, Malajovich and Shub. We prove a continuous analogue of the result of Holt and Klee, namely, we construct a family of polytopes which attain the conjectured order of the largest total curvature. Citation AdvOL-Report #2006/09 Advanced Optimization … Read more

Step decision rules for multistage stochastic programming: a heuristic approach

Stochastic programming with step decision rules, SPSDR, is an attempt to overcome the curse of computational complexity of multistage stochastic programming problems. SPSDR combines several techniques. The first idea is to work with independent experts. Each expert is confronted with a sample of scenarios drawn at random from the original stochastic process. The second idea … Read more

Fast computation of the leastcore and prenucleolus of cooperative games

The computation of leastcore and prenucleolus is an efficient way of allocating a common resource among N players. It has, however, the drawback being a linear programming problem with 2^N-2 constraints. In this paper we show how, in the case of convex production games, generate constraints by solving small size linear programming problems, with both … Read more