A semidefinite relaxation scheme for quadratically constrained

author

  • Salahi
Abstract:

  Semidefinite optimization relaxations are among the widely used approaches to find global optimal or approximate solutions for many nonconvex problems. Here, we consider a specific quadratically constrained quadratic problem with an additional linear constraint. We prove that under certain conditions the semidefinite relaxation approach enables us to find a global optimal solution of the underlying problem in polynomial time .

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Semidefinite relaxation for dominating set

‎It is a well-known fact that finding a minimum dominating set and consequently the domination number of a general graph is an NP-complete problem‎. ‎In this paper‎, ‎we first model it as a nonlinear binary optimization problem and then extract two closely related semidefinite relaxations‎. ‎For each of these relaxations‎, ‎different rounding algorithm is exp...

full text

On Efficient Semidefinite Relaxations for Quadratically Constrained Quadratic Programming

Two important topics in the study of Quadratically Constrained Quadratic Programming (QCQP) are how to exactly solve a QCQP with few constraints in polynomial time and how to find an inexpensive and strong relaxation bound for a QCQP with many constraints. In this thesis, we first review some important results on QCQP, like the S-Procedure, and the strength of Lagrangian Relaxation and the semi...

full text

A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs

We propose a modified alternate direction method for solving convex quadratically constrained quadratic semidefinite optimization problems. The method is a first-order method, therefore requires much less computational effort per iteration than the second-order approaches such as the interior point methods or the smoothing Newton methods. In fact, only a single inexact metric projection onto th...

full text

Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming

We consider relaxations for nonconvex quadratically constrained quadratic programming (QCQP) based on semidefinite programming (SDP) and the reformulation-linearization technique (RLT). From a theoretical standpoint we show that the addition of a semidefiniteness condition removes a substantial portion of the feasible region corresponding to product terms in the RLT relaxation. On test problems...

full text

KKT Solution and Conic Relaxation for Solving Quadratically Constrained Quadratic Programming Problems

To find a global optimal solution to the quadratically constrained quadratic programming problem, we explore the relationship between its Lagrangian multipliers and related linear conic programming problems. This study leads to a global optimality condition that is more general than the known positive semidefiniteness condition in the literature. Moreover, we propose a computational scheme that...

full text

A new semidefinite programming relaxation scheme for a class of quadratic matrix problems

Weconsider a special class of quadraticmatrix optimizationproblemswhich often arise in applications. By exploiting the special structure of these problems, we derive a new semidefinite relaxation which, under mild assumptions, is proven to be tight for a larger number of constraints than could be achieved via a direct approach. We show the potential usefulness of these results when applied to r...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 2  issue None

pages  29- 34

publication date 2011-06

By following a journal you will be notified via email when a new issue of this journal is published.

Keywords

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023