An Interior-Point Method for Approximate Positive Semidefinite Completions
Computational Optimization and Applications
Computational Optimization and Applications
A Note on the Calculation of Step-Lengths in Interior-Point Methods for Semidefinite Programming
Computational Optimization and Applications
On a commutative class of search directions for linear programming over symmetric cones
Journal of Optimization Theory and Applications
Semidefinite Programming Relaxation for NonconvexQuadratic Programs
Journal of Global Optimization
A Polyhedral Approach for Nonconvex Quadratic Programming Problemswith Box Constraints
Journal of Global Optimization
On Copositive Programming and Standard Quadratic Optimization Problems
Journal of Global Optimization
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Computational Experience with Ill-Posed Problems in Semidefinite Programming
Computational Optimization and Applications
DS '99 Proceedings of the Second International Conference on Discovery Science
Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems
Mathematics of Operations Research
SDPARA: semiDefinite programming algorithm paRAllel version
Parallel Computing
Convergence Analysis of an Inexact Infeasible Interior Point Method for Semidefinite Programming
Computational Optimization and Applications
Solving semidefinite programming problems via alternating direction methods
Journal of Computational and Applied Mathematics
A conversion of an SDP having free variables into the standard form SDP
Computational Optimization and Applications
Optimization Methods & Software
Limiting behavior of the Alizadeh-Haeberly-Overton weighted paths in semidefinite programming
Optimization Methods & Software
Clustering for bioinformatics via matrix optimization
Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine
On the long-step path-following method for semidefinite programming
Operations Research Letters
ACM Transactions on Mathematical Software (TOMS)
An inexact spectral bundle method for convex quadratic semidefinite programming
Computational Optimization and Applications
High-performance general solver for extremely large-scale semidefinite programming problems
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
A homotopy method for nonlinear semidefinite programming
Computational Optimization and Applications
Hi-index | 0.00 |
The SDLCP (semidefinite linear complementarity problem) in symmetric matrices introduced in this paper provides a unified mathematical model for various problems arising from systems and control theory and combinatorial optimization. It is defined as the problem of finding a pair $(\X,\Y)$ of $n \times n$ symmetric positive semidefinite matrices which lies in a given $n(n+1)/2$ dimensional affine subspace $\FC$ of $\SC^2$ and satisfies the complementarity condition $\X \bullet \Y = 0$, where $\SC$ denotes the $n(n+1)/2$-dimensional linear space of symmetric matrices and $\X \bullet \Y$ the inner product of $\X$ and $\Y$. The problem enjoys a close analogy with the LCP in the Euclidean space. In particular, the central trajectory leading to a solution of the problem exists under the nonemptiness of the interior of the feasible region and a monotonicity assumption on the affine subspace $\FC$. The aim of this paper is to establish a theoretical basis of interior-point methods with the use of Newton directions toward the central trajectory for the monotone SDLCP.