A PROPERTY OF BICRITERIA AFFINE VECTOR VARIATIONAL INEQUALITIES

Abstract

By a scalarization method, it is proved that both the Pareto solution set and the weak Pareto solution set of a bicriteria affine vector variational inequality have finitely many connected. components provided that a regularity condition is satisfied. An explicit upper bound for the numbers of connected components of the Pareto solution set and the weak. Pareto solution set is obtained. Consequences of the results for bicriteria quadratic vector optimization problems and linear fractional vector optimization problems are discussed in detail. Under an additional assumption on the data set, Theorems 3.1 and 3.2 in this paper solve in the affirmative Question 1 in [17, p. 66] and Question 9.3 in [151 for the case of bicriteria problems without requiring the monotonicity. Besides, the theorems also give a partial solution to Question 2 in [17] about finding an upperboundfor the numbers ofconnected components of the solution sets under investigation.