# American Institute of Mathematical Sciences

July  2014, 10(3): 871-882. doi: 10.3934/jimo.2014.10.871

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

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

Received  October 2011 Revised  July 2013 Published  November 2013

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.
Citation: Ziye Shi, Qingwei Jin. Second order optimality conditions and reformulations for nonconvex quadratically constrained quadratic programming problems. Journal of Industrial & Management Optimization, 2014, 10 (3) : 871-882. doi: 10.3934/jimo.2014.10.871
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