On SOCP-based disjunctive cuts for solving a class of integer bilevel nonlinear programs.

Unlabelled: We study a class of integer bilevel programs with second-order cone constraints at the upper-level and a convex-quadratic objective function and linear constraints at the lower-level. We develop disjunctive cuts (DCs) to separate bilevel-infeasible solutions using a second-order-cone-based cut-generating procedure. We propose DC separation strategies and consider several approaches for removing redundant disjunctions and normalization.

Exact solution approaches for the discrete -neighbor -center problem.

The discrete -neighbor -center problem (d--CP) is an emerging variant of the classical -center problem which recently got attention in literature. In this problem, we are given a discrete set of points and we need to locate facilities on these points in such a way that the maximum distance between each point where no facility is located and its -closest facility is minimized. The only existing algorithms in literature for solving the d--CP are approximation algorithms and two recently proposed heuristics.

An SDP-based approach for computing the stability number of a graph.

Finding the stability number of a graph, i.e., the maximum number of vertices of which no two are adjacent, is a well known NP-hard combinatorial optimization problem.

A computational study of exact subgraph based SDP bounds for Max-Cut, stable set and coloring.

The "exact subgraph" approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational challenge because of the potentially large number of violated subgraph constraints. We introduce a computational framework for these relaxations designed to cope with these difficulties.