Characterizations of weak sharp minima of order one in nonlinear programming
Marcin Studniarski · 2022
This chapter derives a new characterization of weak sharp local minimizers of order one for a standard nonlinear programming problem with constraints of both inequality and equality type. It argues that some additional conditions can be attached to the Kuhn-Tucker conditions, giving a set of conditions which characterize this sort of local minimizers. The chapter also argues that the functions defining equality constraints are differentiable. while the objective function and the functions defining inequality constraints are locally Lipschitzian and have convex directional derivatives. It reviews a characterization of the contingent cone to a set defined by equality and inequality constraints. The chapter presents several theorems characterizing weak sharp local minimizers of order one for nonlinear programming problems.