Matrix analysis
A simple constraint qualification in infinite dimensional programming
Mathematical Programming: Series A and B
A nonlinear equation for linear programming
Mathematical Programming: Series A and B
Partially finite convex programming, part I: quasi relative interiors and duality theory
Mathematical Programming: Series A and B
On adaptive-step primal-dual interior-point algorithms for linear programming
Mathematics of Operations Research
Principal Submatrices, Geometric Multiplicities, and Structured Eigenvectors
SIAM Journal on Matrix Analysis and Applications
Optimization by Vector Space Methods
Optimization by Vector Space Methods
SIAM Journal on Optimization
Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results
Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Distance Matrix Completion by Numerical Optimization
Computational Optimization and Applications
Kernel Matrix Completion by Semidefinite Programming
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Semidefinite programming for discrete optimization and matrix completion problems
Discrete Applied Mathematics
Covariance selection for nonchordal graphs via chordal embedding
Optimization Methods & Software - Mathematical programming in data mining and machine learning
The discretizable molecular distance geometry problem
Computational Optimization and Applications
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Given a nonnegative, symmetric matrix of weights, H, westudy the problem of finding an Hermitian, positive semidefinite matrixwhich is closest to a given Hermitian matrix, A, with respectto the weighting H. This extends the notion of exact matrixcompletion problems in that, H_ij=0 corresponds to theelement A_ij being unspecified (free),while H_ij large in absolute value corresponds to the elementA_ij being approximately specified (fixed).We present optimality conditions, duality theory, and two primal-dualinterior-point algorithms. Because of sparsity considerations, thedual-step-first algorithm is more efficient for a large number of freeelements, while the primal-step-first algorithm is more efficient for alarge number of fixed elements.Included are numerical tests that illustrate the efficiency androbustness of the algorithms