A mathematical programming approach to strong separation in normed spaces

Marco A. Lopez, Soon Yi Wu, Chen Ling, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper deals with an infinite-dimensional optimization approach to the strong separation of two bounded sets in a normed space. We present an approximation procedure, called Algorithm (A), such that a semi-infinite optimization problem must be solved at each step. Its global convergence is established under certain natural assumptions, and a stopping criterion is also provided. The particular case of strong separation in the space Lp(X, A, μ) is approached in detail. We also propose Algorithm (B), which is an implementable modification of Algorithm (A) for separating two bounded sets in Lp([a, b]), with [a, b] being an interval in R. Some illustative computational experience is reported, and a particular stopping criterion is provided for the case of functions of bounded variation in L2([a, b]).
Original languageEnglish
Pages (from-to)211-227
Number of pages17
JournalJournal of Convex Analysis
Volume17
Issue number1
Publication statusPublished - 19 Mar 2010

Keywords

  • Infinite dimensional optimization
  • Semi-infinite programming
  • Strong separation

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this