Semidefinite optimization in discrepancy theory

Exploiting semidefinite relaxations in constraint programming

Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In principle, we use the solution of a semidefinite relaxation to guide the traversal of the search tree, using a limited discrepancy search strategy. Furthermor...

A Semidefinite Optimization Approach to Quadratic Fractional Optimization with a Strictly Convex Quadratic Constraint

In this paper we consider a fractional optimization problem that minimizes the ratio of two quadratic functions subject to a strictly convex quadratic constraint. First using the extension of Charnes-Cooper transformation, an equivalent homogenized quadratic reformulation of the problem is given. Then we show that under certain assumptions, it can be solved to global optimality using semidefini...

Some Applications of Semidefinite Optimization from an Operations Research Viewpoint

New complexity analysis of a full Nesterov-Todd steps IIPM for semidefinite optimization

The Komlos Conjecture Holds for Vector Colorings

The Komlós conjecture in discrepancy theory states that for some constant K and for any m× n matrix A whose columns lie in the unit ball there exists a vector x ∈ {−1,+1} such that ‖Ax‖∞ ≤ K. This conjecture also implies the Beck-Fiala conjecture on the discrepancy of bounded degree hypergraphs. Here we prove a natural relaxation of the Komlós conjecture: if the columns of A are assigned unit v...