Penalty/barrier multiplier methods for convex programming problems

作     者：BenTal, A Zibulevsky, M 

作者机构：Fac. of Indust. Eng. and Management Technion - Israel Inst. of Technol. Haifa 32000 Israel 

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

年 卷 期：1997年第7卷第2期

页      面：347-366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：convex programming augmented Lagrangian 

摘      要：We study a class of methods for solving convex programs, which are based on non-quadratic augmented Lagrangians for which the penalty parameters are functions of the multipliers. This gives rise to Lagrangians which are nonlinear in the multipliers. Each augmented Lagrangian is specified by a choice of a penalty function phi and a penalty-updating function pi. The requirements on pi are mild and allow for the inclusion of most of the previously suggested augmented Lagrangians. More importantly, a new type of penalty/barrier function (having a logarithmic branch glued to a quadratic branch) is introduced and used to construct an efficient algorithm. Convergence of the algorithms is proved for the case of pi being a sublinear function of the dual multipliers. The algorithms are tested on large-scale quadratically constrained problems arising in structural optimization.