Name
Title | ||
|---|---|---|
Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
1997 | 10.1137/S1052623494269035 | SIAM Journal on Optimization |
Keywords | Field | DocType |
interior-point method,linear complementarity problem,linear matrix inequality,semidefinite program,linear program | Discrete mathematics,Combinatorics,Mathematical optimization,Affine space,Matrix (mathematics),Linear space,Positive-definite matrix,Euclidean space,Linear complementarity problem,Semidefinite embedding,Monotone polygon,Mathematics | Journal |
Volume | Issue | ISSN |
7 | 1 | 1052-6234 |
Citations | PageRank | References |
149 | 15.92 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Masakazu Kojima | 1 | 1603 | 222.51 |
| Susumu Shindoh | 2 | 262 | 27.71 |
| Shinji Hara | 3 | 188 | 26.47 |