An adaptive discretization method solving semi-infinite optimization problems with quadratic rate of convergence. (3rd August 2022)

• Record Type: Journal Article
• Authors: Seidel, Tobias; Küfer, Karl-Heinz
• Is Part Of: Optimization. Volume 71:Number 8(2022)
• Page Start: 2211
• Page End: 2239
• Publication Date: 2022-08-03
• Subjects: Semi-infinite programming -- discretization methods -- bi-level optimization -- stationary points -- quadratic convergence; 90C34 -- 41A25 -- 90C31 -- 90C30 -- 9008; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1804566
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: Semi-infinite programming can be used to model a large variety of complex optimization problems. The simple description of such problems comes at a price: semi-infinite problems are often harder to solve than finite nonlinear problems. In this paper, we combine a classical adaptive discretization method developed by Blankenship and Falk [Infinitely constrained optimization problems. J Opt Theory Appl. 1976;19(2):261–281. https://doi.org/10.1007/BF00934096] and techniques regarding a semi-infinite optimization problem as a bi-level optimization problem. We develop a new adaptive discretization method which combines the advantages of both techniques and exhibits a quadratic rate of convergence. We further show that a limit of the iterates is a stationary point, if the iterates are stationary points of the approximate problems.