Nonlinear separation in the image space with applications to penalty methods

Abstract

In this article we analyse a nonlinear separation scheme in the image space associated with an infinite-dimensional cone constrained extremum problem, and, in particular, we consider the applications to nonlinear Lagrangian duality and exact and inexact exterior penalty methods. Duality and exact penalty methods arise from the existence of a regular nonlinear separation, which is shown to be equivalent to a saddle point condition for a generalized Lagrangian function associated with the given problem, while inexact penalty methods are closely related with the existence of an asymptotic nonlinear separation.

Keywords:

• image space
• nonlinear separation
• penalty methods

AMS Subject Classifications::

• 65K05
• 90C48