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Convexification of a Noninferior Frontier
Authors:Goh  C J  Yang  X Q
Institution:(1) Department of Mathematics, University of Western Australia, Nedlands, Western Australia, Australia;(2) Department of Mathematics, University of Western Australia, Nedlands, Western Australia, Australia
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
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