Block-diagonal semidefinite programming hierarchies for 0/1 programming

Lovasz and Schrijver, and later Lasserre, proposed hierarchies of semidefinite programming relaxations for general 0/1 linear programming problems. In this paper these two constructions are revisited and two new, block-diagonal hierarchies are proposed. They have the advantage of being computationally less costly while being at least as strong as the Lovasz-Schrijver hierarchy. Our construction is applied to the stable set problem and experimental results for Paley graphs are reported.Comment: 11 pages, (v2) revision based on suggestions by referee, computation of N+(TH(P_q)) included in Table

Lecture notes: Semidefinite programs and harmonic analysis

Lecture notes for the tutorial at the workshop HPOPT 2008 - 10th International Workshop on High Performance Optimization Techniques (Algebraic Structure in Semidefinite Programming), June 11th to 13th, 2008, Tilburg University, The Netherlands.Comment: 31 page

Semidefinite Programming in Combinatorial and Polynomial Optimization

In the recent years semidefinite programming has become a widely used tool for designing better efficient algorithms for approximating hard combinatorial optimization problems and, more generally, polynomial optimization problems, which deal with optimizing a polynomial objective function over a basic closed semialgebraic set. The underlying paradigm is that, while testing nonnegativity of a polynomial is a hard problem, one can test efficiently whether it can be written as a sum of squares of polynomials, using semidefinite programming. In this note we sketch some of the main mathematical tools that underlie this approach and illustrate its application to some graph problems dealing with maximum cuts, stable sets and graph coloring

Proof Complexity and Beyond

Proof complexity is a multi-disciplinary intellectual endeavor that addresses questions of the general form “how difficult is it to prove certain mathematical facts?” The current workshop focused on recent advances in our understanding of logic-based proof systems and on connections to algorithms, geometry and combinatorics research, such as the analysis of approximation algorithms, or the size of linear or semidefinite programming formulations of combinatorial optimization problems, to name just two important examples

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1