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.Expand

Abstract The question of which partial Hermitian matrices (some entries specified, some free) may be completed to positive definite matrices is addressed. It is shown that if the diagonal entries are… Expand

Contributing Authors. List of Figures. List of Tables. Preface. 1. Introduction H. Wolkowicz, et al. Part I: Theory. 2. Convex Analysis on Symmetric Matrices F. Jarre. 3. The Geometry of Semidefinite… Expand

Semidefinite programming (SDP) relaxations for the quadratic assignment problem (QAP) are derived using the dual of the (homogenized) Lagrangian dual of appropriate equivalent representations of QAP.Expand

Primal-dual pairs of semidefinite programs provide a general framework for the theory and algorithms for the trust region subproblem (TRS) as a parametric eigenvalue problem.Expand

Abstract Characterizations of optimality for the abstract convex program μ = inf {p(x) : g(x) ϵ −S, x ϵ Ω} (P) where S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set,… Expand

Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing , and combinatorial data analysis.Expand