Second order optimality conditions and reformulations for nonconvex quadratically constrained quadratic programming problems

Ziye Shi; Qingwei Jin

doi:10.3934/jimo.2014.10.871

Article Contents

2014, Volume 10, Issue 3: 871-882. Doi: 10.3934/jimo.2014.10.871

This issue Previous Article An alternating linearization method with inexact data for bilevel nonsmooth convex optimization Next Article A nonlinear conjugate gradient method for a special class of matrix optimization problems

Second order optimality conditions and reformulations for nonconvex quadratically constrained quadratic programming problems

Ziye Shi^1, and
Qingwei Jin^2,

1.
Department of Mathematical Sciences, Tsinghua University, Beijing, 100084
2.
Department of Management Science and Engineering, Zhejiang University, Hangzhou, Zhejiang 310058

Received: September 30, 2011

Revised: June 30, 2013

Published: June 2014

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Abstract

In this paper, we present an optimality condition which could determine whether a given KKT solution is globally optimal. This condition is equivalent to determining if the Hessian of the corresponding Largrangian is copositive over a set. To find the corresponding Lagrangian multiplier, two linear conic programming problems are constructed and then relaxed for computational purpose. Under the new condition, we proposed a local search based scheme to find a global optimal solution and showed its effectiveness by three examples.

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Mathematics Subject Classification: 49N15, 49M37, 90C26, 90C20.

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