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Matrix convex functions with applications to weighted centres for semidefinite programming (2005)
| Citations: | 5 - 0 self |
BibTeX
@MISC{Brinkhuis05matrixconvex,
author = {Jan Brinkhuis and Zhi-quan Luo and Shuzhong Zhang},
title = {Matrix convex functions with applications to weighted centres for semidefinite programming},
year = {2005}
}
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Abstract
In this paper, we develop various calculus rules for general smooth matrix-valued functions and for the class of matrix convex (or concave) functions first introduced by Löwner and Kraus in 1930s. Then we use these calculus rules and the matrix convex function − logX to study a new notion of weighted centers for semidefinite programming (SDP) and show that, with this definition, some known properties of weighted centers for linear programming can be extended to SDP. We also show how the calculus rules for matrix convex functions can be used in the implementation of barrier methods for optimization problems involving nonlinear matrix functions.
Keyphrases
matrix convex function semidefinite programming weighted centre calculus rule weighted center matrix convex known property various calculus rule general smooth matrix-valued function linear programming lo wner optimization problem matrix convex function logx nonlinear matrix function new notion
