AN ELLIPSOID TRUST REGION BUNDLE METHOD FOR NONSMOOTH CONVEX MINIMIZATION

作     者：KIWIEL, KC 

出 版 物：《SIAM JOURNAL ON CONTROL AND OPTIMIZATION》 (工业与应用数学会控制与最佳化杂志)

年 卷 期：1989年第27卷第4期

页      面：737-757页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0811[工学-控制科学与工程] 0701[理学-数学] 

主　　题：65K05 90C25 nonsmooth optimization nondifferentiable programming convex programming descent methods ellipsoid algorithm 

摘      要：This paper presents a bundle method of descent for minimizing a convex (possibly nonsmooth) function f of several variables. At each iteration the algorithm finds a trial point by minimizing a polyhedral model of f subject to an ellipsoid trust region constraint. The quadratic matrix of the constraint, which is updated as in the ellipsoid method, is intended to serve as a generalized “Hessian to account for “second-order effects, thus enabling faster convergence. The interpretation of generalized Hessians is largely heuristic, since so far this notion has been made precise by J. L. Goffin only in the solution of linear inequalities. Global convergence of the method is established and numerical results are given.