Convexification of a noninferior frontier

C. J. Goh, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

Abstract

In a recent paper by Li (Ref. 1), a scheme was proposed to convexify an efficient frontier for a vector optimization problem by rescaling each component of the vector objective functions by its p-power. For sufficiently large p, it was shown that the transformed efficient frontier is cone-convex; hence, the usual linear scalarization (or supporting hyperplane) method can be used to find the efficient solutions. An outstanding question remains: What is the minimum value of p such that the efficient frontier can be convexified? In this note, we answer the above question by deriving some theoretical lower bounds for p.
Original languageEnglish
Pages (from-to)759-768
Number of pages10
JournalJournal of Optimization Theory and Applications
Volume97
Issue number3
DOIs
Publication statusPublished - 1 Jan 1998
Externally publishedYes

Keywords

  • Efficient frontier
  • Nonconvex vector optimization
  • Weighted p-norm problems

ASJC Scopus subject areas

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

Cite this