Based on previous explicit computations of universal barrier functions, we describe numerical experiments for solving certain classes of convex optimization problems. The comparison is given of the performance of the classical affine-scaling algorithm with similar algorithm based upon the universal barrier function CitationTo appear in “Computational Optimization and Applications”ArticleDownload View PDF
In the paper we study some well-known cases of nonlinear programming problems, presenting them as instances of Inexact Linear Programming. The class of problems considered contains, in particular, semidefinite programming, second order cone programming and special cases of inexact semidefinite programming. Strong duality results for the nonlinear problems studied are obtained via the Lagrangian duality. … Read more
We explicitly calculate universal barrier functions for cones generated by (weakly) Chebyshev systems over finite sets. We show that universal barrier functions corresponding to Chebyshev systems on intervals are obtained as limits of universal barrier functions of their discretizations. The results are heavily rely upon classical work of M. Krein, A. Nudelman and I.J. Schoenberg … Read more
The aim of this paper is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented making use of two general iscreteapproximation methods. Simultaneously, we discuss the consistenceand the epi-convergence of the asymptotic approximation problem. CitationSchool of … Read more
Cutting plane methods provide the means to solve large scale semidefinite programs (SDP) cheaply and quickly. They can also conceivably be employed for the purposes of re-optimization after branching, or the addition of cutting planes. We give a survey of various cutting plane approaches for SDP in this paper. These cutting plane approaches arise from … Read more