Hunting for a Smaller Convex Subdifferential

Authors:
V. F. Demyanov;V. Jeyakumar
Affiliations:
Applied Mathematics Department, St. Petersburg State University, Staryi Peterhof 198904, Russia/ School of Mathematics, University of New South Wales, Sydney 2052, Australia.;Applied Mathematics Department, St. Petersburg State University, Staryi Peterhof 198904, Russia/ School of Mathematics, University of New South Wales, Sydney 2052, Australia.
Venue:
Journal of Global Optimization
Year:
1997

Citing 4
Cited 4

Shrinking generalized gradients

Non-Linear Analysis
A Lagrange multiplier rule with small convex-valued subdifferentials for nonsmooth problems of mathematical programming involving equality and nonfunctional constraints

Mathematical Programming: Series A and B
Constraint qualifications in quasidifferentiable optimization

Mathematical Programming: Series A and B
A generalized mean-value theorem and optimality conditions in composite nonsmooth minimization

Nonlinear Analysis: Theory, Methods & Applications

The Rise of Nonsmooth Analysis: Its Main Tools

Cybernetics and Systems Analysis
Necessary Optimality Conditions for Bilevel Optimization Problems Using Convexificators

Journal of Global Optimization
A (CF)-mapping of integral functional of locally lipschitz functions

Journal of Global Optimization
Convexificators and strong Kuhn-Tucker conditions

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

Certain useful basic results of the gradient (in the smooth case), the Clarkesubdifferential, the Michel–Penot subdifferential, which is also known asthe "small" subdifferential, and the directional derivative(in the nonsmooth case) are stated and discussed. One of the advantages ofthe Michel–Penot subdifferential is the fact that it is in general "smaller"than the Clarke subdifferential. In this paper it is shown that there existsubdifferentials which may be smaller than the Michel–Penot subdifferentialandwhich have certain useful calculus. It isfurther shown that in the case of quasidifferentiability, the Michel–Penotsubdifferential enjoys calculus whichhold for the Clarke subdifferential only in the regular case.