Linear semidefinite programming problems: regularisation and strong dual formulations

Semidefinite Programming : Formulations and Primal - Dual Interior - Point Methods

Linear Programming ( Lp ) Approaches to Semidefinite Programming ( Sdp ) Problems

Until recently, the study of interior point methods has dominated algorithmic research in semidefinite programming (SDP). From a theoretical point of view, these interior point methods offer everything one can hope for; they apply to all SDP’s, exploit second order information and offer polynomial time complexity. Still for practical applications with many constraints k, the number of arithmeti...

A Linear Programming Approach to Semidefinite Programming Problems

A semidefinite programming problem can be regarded as a convex nonsmooth optimization problem, so it can be represented as a semi-infinite linear programming problem. Thus, in principle, it can be solved using a cutting plane approach; we describe such a method. The cutting plane method uses an interior point algorithm to solve the linear programming relaxations approximately, because this resu...

Semi-infinite linear programming approaches to semidefinite programming problems∗

Interior point methods, the traditional methods for the SDP , are fairly limited in the size of problems they can handle. This paper deals with an LP approach to overcome some of these shortcomings. We begin with a semi-infinite linear programming formulation of the SDP and discuss the issue of its discretization in some detail. We further show that a lemma due Pataki on the geometry of the SDP...

Linear, Semidefinite Programming and Randomization Methods for Combinatorial Optimization Problems