An equilibrium theorem for subdifferential
Yutaka Kimura, Daishi Kuroiwa, Kensuke Tanaka · Journal of Information and Optimization Sciences · 1997
In this paper, for a convex and continuous function and a subset of constraints, we investigate the equilibrium theorem for the subdifferential. At first, in the case where the subset is w-compact and convex, we show that the equilibrium theorem holds under the convexity of subdifferential and the tangential condition. Moreover, in the case where the whole space is reflexive and the subset is closed and convex (noncompact), we show that the equilibrium theorem holds under the convexity of subdifferential, the tangential condition, and a condition for directional derivative.