Abstract and Applied Analysis

$\sigma$-Porosity in monotonic analysis with applications to optimization

A. M. Rubinov

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Abstract

We introduce and study some metric spaces of increasing positively homogeneous (IPH) functions, decreasing functions, and conormal (upward) sets. We prove that the complements of the subset of strictly increasing IPH functions, of the subset of strictly decreasing functions, and of the subset of strictly conormal sets are σ-porous in corresponding spaces. Some applications to optimization are given.

Article information

Source
Abstr. Appl. Anal., Volume 2005, Number 3 (2005), 287-305.

Dates
First available in Project Euclid: 25 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1122298430

Digital Object Identifier
doi:10.1155/AAA.2005.287

Mathematical Reviews number (MathSciNet)
MR2197121

Zentralblatt MATH identifier
1102.46016

Citation

Rubinov, A. M. $\sigma$-Porosity in monotonic analysis with applications to optimization. Abstr. Appl. Anal. 2005 (2005), no. 3, 287--305. doi:10.1155/AAA.2005.287. https://projecteuclid.org/euclid.aaa/1122298430


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