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Entanglement witnesses and semidefinite programming
Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2004We study the application of sums of squares decompositions and semidefinite programming in the formulation of computational criteria for distinguishing entangled from separable quantum states. A hierarchy of tests is obtained, the simplest of which corresponds to the well-known positive partial transpose (PPT) sufficient criterion, with the more ...
Pablo A. Parrilo +2 more
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A robust algorithm for semidefinite programming
Optimization Methods and Software, 2012Current successful methods for solving semidefinite programs SDPs are based on primal–dual interior-point approaches. These usually involve a symmetrization step to allow for application of Newton's method followed by block elimination to reduce the size of the Newton equation.
Xuan Vinh Doan +2 more
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A sensitivity result for semidefinite programs
Operations Research Letters, 2004The authors consider the perturbation of solutions of linear semidefinite problems subjected to small changes of the data. A self-contained proof of the differentiability of unique and strictly complementary solutions is given. Furthermore a new characterization of the derivatives of the solution map as solutions of a nonsingular system of linear ...
Roland W. Freund, Florian Jarre
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Semidefinite Programming in the Space of Partial Positive Semidefinite Matrices
SIAM Journal on Optimization, 2003Summary: We build upon the work of \textit{M. Fukuda} et al. [SIAM J. Optim. 11, 647--674 (2001; Zbl 1010.90053)] and \textit{K. Nakata} et al. [Math. Program. 95, No. 2(B), 303--327 (2003; Zbl 1030.90081)], in which the theory of partial positive semidefinite matrices was applied to the semidefinite programming (SDP) problem as a technique for ...
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Statistical inference of semidefinite programming
Mathematical Programming, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Embedding methods for semidefinite programming
Optimization Methods and Software, 2012This paper is devoted to the study of embedding methods for semidefinite programming problems using the duals formulated by Ramana, Tuncel, and Wolkowicz in 1997. Specifically, if we solve a semidefinite programming problem PD in either standard primal or dual form, a dual problem of PD, which guarantees strong duality i.e.
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