On the local convergence of a predictor-corrector method for semidefinite programming

作     者：Ji, J Potra, FA Sheng, RQ 

作者机构：Valdosta State Univ Dept Math & Comp Sci Valdosta GA 31698 USA Univ Maryland Baltimore Cty Dept Math & Stat Baltimore MD 21250 USA Lucent Technol Inc Lisle IL 60532 USA Univ Iowa Iowa City IA 52242 USA 

出 版 物：《SIAM JOURNAL ON OPTIMIZATION》 (工业与应用数学会最优化杂志)

年 卷 期：1999年第10卷第1期

页      面：195-210页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：semidefinite programming interior point method superlinear convergence 

摘      要：We study the local convergence of a predictor-corrector algorithm for semidefinite programming problems based on the Monteiro-Zhang unified direction whose polynomial convergence was recently established by Monteiro. Under strict complementarity and nondegeneracy assumptions superlinear convergence with Q-order 1.5 is proved if the scaling matrices in the corrector step have bounded condition number. A version of the predictor-corrector algorithm enjoys quadratic convergence if the scaling matrices in both predictor and corrector steps have bounded condition numbers. The latter results apply in particular to algorithms using the Alizadeh-Haeberly-Overton (AHO) direction since there the scaling matrix is the identity matrix.