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K.M. Anstreicher(kurtanstreicheruiowa.edu) Abstract: We consider semidefinite optimization problems that include constraints that G(x) and H(x) are positive semidefinite (PSD), where the components of the symmetric matrices G(x) and H(x) are affine functions of an nvector x. In such a case we obtain a new constraint that a matrix K(x,X) is PSD, where the components of K(x,X) are affine functions of x and X, and X is an nxn matrix that is a relaxation of xx'. The constraint that K(x,X) is PSD is based on the fact that the Kronecker product of G(x) and H(x) must be PSD. This construction of a constraint based on the Kronecker product generalizes the construction of an RLT constraint from two linear inequality constraints, and also the construction of an SOCRLT constraint from one linear inequality constraint and a secondorder cone constraint. We show how the Kronecker product constraint obtained from two secondorder cone constraints can be efficiently used to computationally strengthen the semidefinite programming relaxation of the twotrustregion subproblem. Keywords: Semidefinite optimization, nonconvex quadratic programming, trustregion subproblem Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Category 2: Nonlinear Optimization (Quadratic Programming ) Category 3: Global Optimization (Theory ) Citation: Dept. of Management Sciences, University of Iowa, Iowa City, IA 52242, June, 2016. Download: [PDF] Entry Submitted: 06/06/2016 Modify/Update this entry  
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