Convexification of a Noninferior Frontier

C. J. Goh and X. Q. Yang
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C. J. Goh: University of Western Australia
X. Q. Yang: University of Western Australia

Journal of Optimization Theory and Applications, 1998, vol. 97, issue 3, No 11, 759-768

Abstract: 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.

Keywords: Nonconvex vector optimization; weighted p-norm problems; efficient frontier (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022654528902

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