Solving semidefinite-quadratic-linear programs using SDPT3

Solving semidefinite-quadratic-linear programs using SDPT3

This paper discusses computational experiments with linear optimization problems involving semidefinite, quadratic, and linear cone constraints (SQLPs). Many test problems of this type are solved using a new release of SDPT3, a Matlab implementation of infeasible primal-dual path-following algorithms. The software developed by the authors uses Mehrotratype predictor-corrector variants of interi...

Solving semidefinite programs using preconditioned conjugate gradients

An Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

Approximating Quadratic Programs with Semidefinite Relaxations

Given an arbitrary matrix A in which all of the diagonal elements are zero, we would like to find x1, x2, . . . , xn ∈ {−1, 1} such that ∑n i=1 ∑n j=1 aijxixj is maximized. This problem has an important application in correlation clustering, and is also related to the well-known inequality of Grothendieck in functional analysis. While solving quadratic programs is NP-hard, we can approximate th...

On the implementation and usage of SDPT3 – a Matlab software package for semidefinite-quadratic-linear programming, version 4.0

This software is designed to solve conic programming problems whose constraintcone is a product of semidefinite cones, second-order cones, nonnegative orthants andEuclidean spaces; and whose objective function is the sum of linear functions andlog-barrier terms associated with the constraint cones. This includes the special caseof determinant maximization problems with linear ma...