Characterizations of the approximate solution sets of nonsmooth optimization problems and its applications
Tóm tắt
The concept of
$$\varphi $$
-strongly preinvex functions is introduced, and some properties of
$$\varphi $$
-strongly preinvex functions are given. Several new and simple characterizations of the approximate solution sets for nonsmooth optimization problems with
$$\varphi $$
-strong preinvexity are obtained. We establish the relationships between the solutions of Minty-type variational-like inequalities and the approximate solutions of optimization problems. And applying the obtained results, we give the characterizations of the solution sets for the Minty-type variational-like inequalities.
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