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Computational Complexity of Decomposing a Symmetric Matrix as a Sum of Positive Semidefinite and Diagonal Matrices
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive-semidefinite matrix and a diagonal matrix. Such...
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Graph coloring and semidefinite rank
This paper considers the interplay between semidefinite programming, matrix rank, and graph coloring. Karger et al. (J ACM 45(2):246–265, 1998) give...
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Partial trace inequalities for partial transpose of positive semidefinite block matrices
Li (Algebra 71:2823–2838, 2023) recently obtained several improvements on some partial trace inequalities for positive semidefinite block matrices....
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New semidefinite relaxations for a class of complex quadratic programming problems
In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in...
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IPRSDP: a primal-dual interior-point relaxation algorithm for semidefinite programming
We propose an efficient primal-dual interior-point relaxation algorithm based on a smoothing barrier augmented Lagrangian, called IPRSDP, for solving...
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A generalized relaxed block positive-semidefinite splitting preconditioner for generalized saddle point linear system
In this paper, based on the block positive-semidefinite splitting (BPS) preconditioner studied recently and the relaxation technique, a generalized...
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A simple proof of second-order sufficient optimality conditions in nonlinear semidefinite optimization
In this note, we present an elementary proof for a well-known second-order sufficient optimality condition in nonlinear semidefinite optimization...
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A Semidefinite Relaxation Method for Linear and Nonlinear Complementarity Problems with Polynomials
This paper considers semidefinite relaxation for linear and nonlinear complementarity problems. For some particular copositive matrices and tensors,...
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A stabilized sequential quadratic semidefinite programming method for degenerate nonlinear semidefinite programs
In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs...
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Second-order cone and semidefinite methods for the bisymmetric matrix approximation problem
Approximating the closest positive semi-definite bisymmetric matrix using the Frobenius norm to a data matrix is important in many engineering...
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DC Semidefinite programming and cone constrained DC optimization I: theory
In this two-part study, we discuss possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear...
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T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization
We study T-semidefinite programming (SDP) relaxation for constrained polynomial optimization problems (POPs). T-SDP relaxation for unconstrained POPs...
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A semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics
We propose an algorithm for computing the projection of a symmetric second-order tensor onto the cone of negative semidefinite symmetric tensors with...
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A Predictor-Corrector Algorithm for Semidefinite Programming that Uses the Factor Width Cone
We propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve...
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Random Projections for Semidefinite Programming
Random projections can reduce the dimensionality of point sets while kee** approximate congruence. Applying random projections to optimization...
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Understanding Badly and Well-Behaved Linear Matrix Inequalities Via Semi-infinite Optimization
In this paper, we use a linear semi-infinite optimization approach to study badly and well-behaved linear matrix inequalities. We utilize a result on...
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An efficient primal-dual interior point algorithm for convex quadratic semidefinite optimization
We introduce a primal-dual interior point algorithm for convex quadratic semidefinite optimization. This algorithm is based on an extension of the...
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A New Smooth NCP Function for Solving Semidefinite Nonlinear Complementarity Problems
In this paper, we propose to solve semidefinite nonlinear complementarity problems (NCP) associated to a nonlinear matrix function , by a...
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A Relaxed Interior Point Method for Low-Rank Semidefinite Programming Problems with Applications to Matrix Completion
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside...
