On Lagrange Multiplier Theorems for Non-smooth Optimization for a Large Class of Variational Models in Banach Spaces

Abstract

This article develops optimality conditions for a large class of non-smooth variational models. The main results are based on standard tools of functional analysis and calculus of variations. Firstly we address a model with equality constraints and, in a second step, a more general model with equality and inequality constraints, always in a general Banach space context. We highlight some novelties are introduced related to the proof procedures developed in this text, which are in general softer than those concerning the present literature.