Path-following barrier and penalty methods for linearly constrained problems

作     者：Al-Mutairi, D. Grossmann, C. Tuan, Vu Kim 

作者机构：Kuwait University Department of Statistics and Operations Research Kuwait University Department of Mathematics and Computer Science TU Dresden Germany 

出 版 物：《Optimization》 (Optimization)

年 卷 期：2000年第48卷第3期

页      面：353-374页

学科分类：0820[工学-石油与天然气工程] 12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 0811[工学-控制科学与工程] 

基　　金：Kuwait University(SM-153) 

主　　题：Barrier methods Complexity Convex programming Interior-point methods Newton's method Pathfollowing Penalty methods SUMT 

摘      要：In the present paper some barrier and penalty methods (e.g., logarithmic barriers, SUMT, exponential penalties), which define a continuously differentiable primal and dual path, applied to linearly constrained convex problems are studied. In particular, the radius of convergence of Newton s method depending on the barrier and penalty parameter is estimated. Unlike using self-concordance properties the convergence bounds are derived by direct estimations of the solutions of the Newton equations. The obtained results establish parameter selection rules which guarantee the overall convergence of the considered barrier and penalty techniques with only a finite number of Newton steps at each parameter level. Moreover, the obtained estimates support scaling method which uses approximate dual multipliers as available in barrier and penalty methods. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.