On the Slater condition for the SDP relaxations of nonconvex sets

Authors:
Levent TunçEl
Affiliations:
Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ont., Canada N2L 3G1
Venue:
Operations Research Letters
Year:
2001

Citing 5
Cited 2

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

Journal of the ACM (JACM)
Semidefinite programming relaxations for the graph partitioning problem

Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Strong Duality for Semidefinite Programming

SIAM Journal on Optimization
Cones of Matrices and Successive Convex Relaxations of Nonconvex Sets

SIAM Journal on Optimization
Semidefinite Programming Relaxation for NonconvexQuadratic Programs

Journal of Global Optimization

A new approach to the stable set problem based on ellipsoids

IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Strong duality and minimal representations for cone optimization

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We prove that all results determining the dimension and the affine hull of feasible solutions of any combinatorial optimization problem, and various more general nonconvex optimization problems, directly imply the existence of the Slater points for a very wide class of semidefinite programming relaxations of these nonconvex problems. Our proofs are very concise, constructive and elementary.