TY - JOUR

T1 - Value functions, domination cones and proper efficiency in multicriteria optimization

AU - Henig, Mordechai I.

PY - 1990/2

Y1 - 1990/2

N2 - In the absence of a clear 'objective' value function, it is still possible in many cases to construct a domination cone according to which efficient (nondominated) solutions can be found. The relations between value functions and domination cones and between efficiency and optimality are analyzed here. We show that such cones must be convex, strictly supported and, frequently, closed as well. Furthermore, in most applications 'potential' optimal solutions are equivalent to properly efficient points. These solutions can often be produced by maximizing with respect to a class of concave functions or, under convexity conditions, a class of affine functions.

AB - In the absence of a clear 'objective' value function, it is still possible in many cases to construct a domination cone according to which efficient (nondominated) solutions can be found. The relations between value functions and domination cones and between efficiency and optimality are analyzed here. We show that such cones must be convex, strictly supported and, frequently, closed as well. Furthermore, in most applications 'potential' optimal solutions are equivalent to properly efficient points. These solutions can often be produced by maximizing with respect to a class of concave functions or, under convexity conditions, a class of affine functions.

UR - http://www.scopus.com/inward/record.url?scp=0025384098&partnerID=8YFLogxK

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AN - SCOPUS:0025384098

SN - 0025-5610

VL - 46

SP - 205

EP - 217

JO - Mathematical Programming

JF - Mathematical Programming

IS - 2

ER -