Arcwise cone-quasiconvex multicriteria optimization

The role played by the generalized convexity in optimization is nowadays well recognized. In this paper we introduce a new concept of quasiconvexity for vector functions, which is shown to have some interesting applications in multicriteria optimization, especially as regards the Pareto reducibility and the strong contractibility of the efficient outcome set. The notion of Pareto reducibility, introduced by Popovici in [8], allows one to reduce the complexity of a multicriteria problem by considering new problems obtained from the original one by selecting a certain number of criteria. More precisely, a multicriteria optimization problem is said to be Pareto reducible if its weakly efficient solutions actually are efficient solutions for the problem itself or for a subproblem obtained from it by selecting certain criteria. In [9] some results concerning the Pareto reducibility and the contractibility of efficient sets have been established for multicriteria optimization problems involving lexicographic quasiconvex objective functions. Our paper aims to extend these results