We propose a new interior-point-based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices....

The aim of this monograph is to provide a Discussion of the Foundations of Semidefinite Programming and its Applications, as well as some Applications and Extensions, which were developed after the original book was written.Expand

These new relaxations, and their duals, satisfy the Slater constraint qualification, and so can be solved numerically using primal-dual interior-point methods.Expand

The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear… Expand

A primal-dual interior-point algorithm is introduced that solves an equivalent (quadratic objective function) semidefinite programming problem (SDP) and demonstrates the efficiency and robustness of this approach.Expand

A dual simplex type method is studied that solves (TRS) as a parametric eigenvalue problem and the essential cost of the algorithm is the matrix-vector multiplication and, thus, sparsity can be exploited.Expand

This paper surveys some of the most important techniques, applications, and methods regarding the quadratic assignment problem and focuses on recent developments.Expand