Convergence of a Three-Dimensional Dwindling Filter Algorithm Without Feasibility Restoration Phase. (3rd March 2016)

• Record Type: Journal Article
• Authors: Gu, Chao; Zhu, Detong
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 3(2016)
• Page Start: 324
• Page End: 341
• Publication Date: 2016-03-03
• Subjects: Feasibility restoration phase -- global convergence -- Lagrangian function -- modified limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) updating -- three-dimensional dwindling filter; 90C30 -- 65K05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2015.1133643
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we propose a three-dimensional dwindling filter algorithm for general nonlinear programming. The envelope of the three-dimensional dwindling filter becomes thinner and thinner as the step size approaches zero so that the new filter has more flexibility for the acceptance of the trial step size. Moreover, we show that the feasibility restoration phase, which is always used in traditional filter method, is not needed. The modified limited memory Broyden-Fletcher-Goldfarb-Shanno method is employed in the algorithm, and the update matrices are positive definite when the Lagrangian function is a general convex function. Under mild conditions, the global convergence of the new algorithm is analyzed. The primary numerical experiments are reported to show effectiveness of the proposed algorithm.