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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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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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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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New Hilbert–Schmidt norm inequalities for positive semidefinite matrices
Let A and B be positive semidefinite matrices, and let X be any matrix. As a generalization of an earlier Hilbert–Schmidt norm inequality, we prove...
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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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A Unitarily Invariant Norm Inequality for Positive Semidefinite Matrices and a Question of Bourin
In this article, we obtain a new unitarily invariant norm inequality for positive semidefinite matrices. In fact, we prove that if A and B are...
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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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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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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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Further unitarily invariant norm inequalities for positive semidefinite matrices
In this paper, we prove further unitarily invariant norm inequalities for positive semidefinite matrices. These inequalities generalize earlier...
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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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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 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 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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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,...