An Interior-Point Method for Semidefinite Programming
- C. Helmberg, F. Rendl, R. Vanderbei, Henry Wolkowicz
- MathematicsSIAM Journal on Optimization
- 1 May 1996
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....
Semidefinite Programming Relaxations for the Quadratic Assignment Problem
- Qing Zhao, S. Karisch, F. Rendl, Henry Wolkowicz
- MathematicsJournal of combinatorial optimization
- 1 March 1998
These new relaxations, and their duals, satisfy the Slater constraint qualification, and so can be solved numerically using primal-dual interior-point methods.
Positive definite completions of partial Hermitian matrices
Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming
- A. Alfakih, A. Khandani, Henry Wolkowicz
- Computer Science, MathematicsComputational optimization and applications
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.
Handbook of semidefinite programming : theory, algorithms, and applications
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.
Regularizing the Abstract Convex Program
A semidefinite framework for trust region subproblems with applications to large scale minimization
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.
SIAM Journal on Optimization
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…
Strong Duality for Semidefinite Programming
The relationships among various duals are discussed and a unified treatment for strong duality in semidefinite programming is given.
The Quadratic Assignment Problem: A Survey and Recent Developments
- P. Pardalos, F. Rendl, Henry Wolkowicz
- Computer Science, MathematicsQuadratic Assignment and Related Problems
This paper surveys some of the most important techniques, applications, and methods regarding the quadratic assignment problem and focuses on recent developments.