We study subdifferential conditions of the calmness property for multifunctions representing convex constraint systems in a Banach space. Extending earlier work in finite dimensions [R. Henrion and J. Outrata, J. Math. Anal. Appl., 258 (2001), pp. 110–130], we show that, in contrast to the stronger Aubin property of a multifunction (or metric regularity of its inverse), calmness can be ensured ...

-In this paper, we investigate some properties of Michel Penot subdifferentials of locally Lipschitz functions and establish Lagrange multiplier rule in terms of Michel-Penot subdifferentials for nonsmooth mathematical programming problem. Key-Words: Nonsmooth optimization; approximate subdifferentials; generalized gradient; Michel Penot subdifferential; Banach space.

‎This paper proposes a new form of optimization problem which is a two-level programming problem with infinitely many lower level constraints‎. ‎Firstly‎, ‎we consider some lower level constraint qualifications (CQs) for this problem‎. ‎Then‎, ‎under these CQs‎, ‎we derive formula for estimating the subdifferential of its valued function‎. ‎Finally‎, ‎we present some necessary optimality condit...

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...