Annales Mathematiques Africaines


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Contenu > Anciens Numéros > Volume_2

Primal-dual Interior Point Algorithms for Semidefinite Optimization Based on a Kernel Function with Quadratic Growth Rate



A. Coulibaly

D. P. Tuo


UFR Mathématiques - Informatique
Université de Cocody, 22 BP 582 Abidjan 22, Côte d'Ivoire



Mathematics Subject Classifications: 90C22, 90C51 .
Key words: semidefinite optimization, interior-point algorithm, large-and small-update methods, iteration bound.

Abstract:


Interior-point methods (IPMs) for semidefinite optimization (SDO) have been studied intensively, due to their polynomial complexity and practical efficiency. Recently, J.Peng et al.peng1,peng2 introduced so-called self-regular kernel (and barrier) functions and designed primal-dual interior-point algoritms based on self-regular proximity for linear optimization (LO) problems.They have also extended the approach for LO to SDO. In this paper we present a primal-dual interior-point algorithm for SDO problems based on a kernel function with quadratic growth rate which was a $3th$ in bai2. The kernel function in this paper is self-regular. We derive the complexity analysis for algorithms with large-and small-update methods. The complexity bounds are MATH and MATH, Respectively, which are as good as those in linear case.


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