CONVEXIFICATION OF A NONINFERIOR FRONTIER

In a recent paper by Li (Ref. 1), a scheme was proposed to convexify a n efficient frontier for a vector optimization problem by rescaling ea ch component of the vector objective functions by its p-power. For suf ficiently large p, it was shown that the transformed efficient frontie r is cone-convex; hence, the usual linear scalarization (or supporting hyperplane) method can be used to find the efficient solutions. An ou tstanding question remains: What is the minimum value of p such that t he efficient frontier can be convexified? In this note, we answer the above question by deriving some theoretical lower bounds for p.