Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Convex Analysis 17 (2010), No. 1, 211--227
Copyright Heldermann Verlag 2010

A Mathematical Programming Approach to Strong Separation in Normed Spaces

Marco A. López
Dept. of Statistics and Operations Research, Alicante University, Ap. de Correos 99, 03080 Alicante, Spain

Soon-Yi Wu
National Cheng Kung University, Tainan, Taiwan

Chen Ling
Zhejiang University of Finance and Economics, Hangzhou, P. R. China

Liqun Qi
Polytechnic University of Hong Kong, Hong Kong, P. R. China


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 $L_{p} (\mathbb{X}, \mathcal{A}, \mu )$ is approached in detail. We also propose Algorithm (B), which is an implementable modification of Algorithm (A) for separating two bounded sets in $L_{p}([a,b])$, with $[a,b]$ being an interval in $\mathbb{R}$. Some illustative computational experience is reported, and a particular stopping criterion is provided for the case of functions of bounded variation in $L_{2}([a,b])$.

Keywords: Strong separation, infinite dimensional optimization, semi-infinite programming.

MSC: 90C48, 46A22, 90C90

[ Fulltext-pdf  (178  KB)] for subscribers only.