Characterizations and applications of prequasi-invex functions

X. M. Yang, Xiaoqi Yang, K. L. Teo

Research output: Journal article publicationJournal articleAcademic researchpeer-review

66 Citations (Scopus)

Abstract

In this paper, two new types of generalized convex functions are introduced. They are called strictly prequasi-invex functions and semistrictly prequasi-invex functions. Note that prequasi-invexity does not imply semistrict prequasi-invexity. The characterization of prequasi-invex functions is established under the condition of lower semicontinuity, upper semicontinuity, and semistrict prequasi-invexity, respectively. Furthermore, the characterization of semistrictly prequasi-invex functions is also obtained under the condition of prequasi-invexity and lower semicontinuity, respectively. A similar result is also obtained for strictly prequasi-invex functions. It is worth noting that these characterizations reveal various interesting relationships among prequasi-invex, semistrictly prequasi-invex, and strictly prequasi-invex functions. Finally, prequasi-invex, semistrictly prequasi-invex, and strictly prequasi-invex functions are used in the study of optimization problems.
Original languageEnglish
Pages (from-to)645-668
Number of pages24
JournalJournal of Optimization Theory and Applications
Volume110
Issue number3
DOIs
Publication statusPublished - 1 Jan 2000

Keywords

  • Optimization
  • Prequasi-invex functions
  • Semicontinuity
  • Semistrictly prequasi-invex functions
  • Strictly prequasi-invex functions

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Cite this