A CONVEXITY-BASED EFFICIENT-POINT STRATEGY FOR MULTICRITERIA OPTIMIZATION

Given a set of axioms concerning preferences, and a finite number of specific preference responses (data) from the decision maker, the unanimous order is the order which ranks one alternative over another if and only if every preference order which satisfies the axioms and is consistent with the data would also rank the alternatives this way. A general efficient-point strategy is a strategy in which efficient (nondominated) points of a suitable unanimous order are sought. Examples of efficient-point strategies are multiobjective (vector) optimization, and the various stochastic dominance approaches. In this thesis, the unanimous order corresponding to axioms of preference convexity (quasi-concave value function) is constructed, and extensions of nonlinear programming techniques are developed under which efficient points of such an order may be calculated