Tamaki Tanaka

On Saddle Points of Multiobjective Functions

This paper is concerned with existence theorems for cone-saddle points of vector-valued functions in finite dimensional Euclidean spaces. By means of vector variational-like inequalities, we first characterize a vector saddle point problem and obtain the existence result under some conditions on the subdifferentiable of the vector-valued function. The continuity and convexity assumptions on the objective function are then relaxed.

On Minimax and Maximin Values in Multicriteria Games

The paper is concerned with a multicriteria game whose payoff takes its values in an ordered vector space. As compare with usual single-criterion games, useful results in such classical games do not always hold as to multicriteria games. For example, minimax and maximin values are coincident under certain conditions in usual single-criterion games, but their values are not always coincident under similar conditions in multicriteria games. Therefore, in this paper, we propose a certain coincidence condition on minimax and maximin values under suitable setting in multicriteria games.

On Inherited Properties for Vector-Valued Multifunctions

In this paper, we consider several kinds of convexity and semicontinuity of multifunctions with respect to ordering cones, and we investigate inherited properties of convexity and semicontinuity through scalarization of multifunctions. We introduce four kinds of scalarizing functions to characterize images of a multifunction by using Tchebyshev scalarization; these (real-valued) scalarizing functions have the same sorts of convexity and semicontinuity which correspond to those of parent multifunctions.