On the Cone of Tangents with Applications to Mathematical Programming.

摘要

In the study the authors present a unifying framework for the cone of tangents to an arbitrary set and some of its applications. The authors highlight the significance of this cone and its polar both from the point of differentiability and subdifferentiability theory and the point of view of mathematical programming. This leads to a generalized definition of a subgradient which extends the well-known definition from the convex function to the nonconvex case. As an application,necessary optimality conditions are developed for a min-max problem and it is shown that these conditions are also sufficient under moderate convexity assumptions. Finally developed are constraint qualifications in this framework. (Modified author abstract)