AN INTERIOR POINT APPROACH FOR SEMIDEFINITE OPTIMIZATION USING NEW PROXIMITY FUNCTIONS

Kernel functions play an important role in interior point methods (IPMs) for solving linear optimization (LO) problems to define a new search direction. In this paper, we consider primal-dual algorithms for solving Semidefinite Optimization (SDO) problems based on a new class of kernel functions def...

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Bibliographic Details
Published in:Asia-Pacific journal of operational research 2009-06, Vol.26 (3), p.365-382
Main Author: PEYGHAMI, M. REZA
Format: Article
Language:English
Subjects:
Approximation
Linear equations
Operations research
Optimization
Optimization algorithms
Studies
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Summary:Kernel functions play an important role in interior point methods (IPMs) for solving linear optimization (LO) problems to define a new search direction. In this paper, we consider primal-dual algorithms for solving Semidefinite Optimization (SDO) problems based on a new class of kernel functions defined on the positive definite cone $\mathcal{S}_{++}^{n\times n}$ . Using some appealing and mild conditions of the new class, we prove with simple analysis that the new class-based large-update primal-dual IPMs enjoy an $O(\sqrt{n}\, {\rm log}\, n\, {\rm log}\, \frac{n}{\varepsilon})$ iteration bound to solve SDO problems with special choice of the parameters of the new class.
ISSN:0217-5959
1793-7019
0217-5959
DOI:10.1142/S0217595909002250