The paper is devoted to the classical variational problem with a nonsmooth integrand of functional be minimized. supposed subdifferentiable. Under some natural conditions subdifferentiability considered proved. finding subdifferential descent direction solved and method applied solve original problem. algorithm developed demonstrated by examples.

We derive a new pointwise characterization of the subdifferential of the total variation (TV) functional. It involves a full trace operator which maps certain L vectorfields to integrable functions with respect to the total variation measure of the derivative of a bounded variation function. This full trace operator extents a notion of normal trace, frequently used, for example, to characterize...

We collect here some known results on the subdifferential of one-homogeneous functionals, which are anisotropic and nonhomogeneous variants of the total variation, and establish a new relationship between Lebesgue points of the calibrating field and regular points of the level lines of the corresponding calibrated function.

We use variational methods to provide a concise development of a number of basic results in convex and functional analysis. This illuminates the parallels between convex analysis and smooth subdifferential theory. 1. The purpose of this note is to give a concise and explicit account of the following folklore: several fundamental theorems in convex analysis such as the sandwich theorem and the F...

The aim of the present work is to use a metric intersection formula estimate subdifferential marginal function in convex setting. This includes many interesting situations parametric programming, including polyhedral one. It expressed terms objective and constrained multivalued mapping which govern program.

In this paper we study the nonsmooth semi-infinite programming problem with inequality constraints. First, we consider the notions of local cone approximation $Lambda$ and $Lambda$-subdifferential. Then, we derive the Karush-Kuhn-Tucker optimality conditions under the Abadie and the Guignard constraint qualifications.

This paper studies the convex multiobjective optimization problem with vanishing constraints‎. ‎We introduce a new constraint qualification for these problems‎, ‎and then a necessary optimality condition for properly efficient solutions is presented‎. ‎Finally by imposing some assumptions‎, ‎we show that our necessary condition is also sufficient for proper efficiency‎. ‎Our results are formula...