A Fritz John optimality condition using the approximate subdifferential
type: Item
instance of: scholarly article
title: A Fritz John optimality condition using the approximate subdifferential
zbMATH Open document ID: 0807.49023
DOI: 10.1007/BF02191853
author: B. M. Glover
author: B. D. Craven
published in: Journal of Optimization Theory and Applications
publication date: 1995-03-01T00:00:00Z
review text: The main result of the paper is the derivation of a Fritz John type first-order optimality condition for the following optimization problem: (P) \(\min f(x)\) s.t. \(-g(x)\in S\). Here \(X\) and \(Y\) are Banach spaces, \(Y\) is separable, \(S\subset Y\) is a closed convex cone, \(f: X\to R\) and \(g: X\to Y\) are locally Lipschitz functions. An additional assumption on \(S\) is made in order to derive the conditions for optimality: either the interior of \(S\) is not empty or \(Y\) is finite-dimensional. Instead of using the Clarke subdifferential to establish the optimality conditions, the authors use the approximate subdifferential. A discussion of the properties of the approximate subdifferential for locally Lipschitz functions is included.
Mathematics Subject Classification ID: 49K27
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 638719
zbMATH Keywords: nonsmooth analysis
zbMATH Keywords: nondifferential programming
zbMATH Keywords: Fritz John type first- order optimality condition
zbMATH Keywords: approximate subdifferential
zbMATH Keywords: Lipschitz functions
reviewed by: Eduardo Casas
MaRDI profile type: Publication
cites work: Optimization and nonsmooth analysis
cites work: Approximate Subdifferentials and Applications. I: The Finite Dimensional Theory
cites work: Approximate subdifferentials and applications II
cites work: Approximate subdifferentials and applications 3: the metric theory
cites work: Proximal Analysis and Approximate Subdifferentials
cites work: Maximum principle in the problem of time optimal response with nonsmooth constraints
cites work: Generalized differentials of nonsmooth functions, and necessary conditions for an extremum
cites work: Q3896139
cites work: Q3952709
cites work: Q3785473
cites work: Q4036809
cites work: Lagrange Multipliers in Stochastic Programming
cites work: On the regularity condition for the extremal problem under locally Lipschitz inclusion constraints
cites work: Subdifferentials of nonconvex vector-valued functions
cites work: The approximate subdifferential of composite functions
cites work: Lagrange multiplers for pareto nonsmooth programming problems in banach spaces
cites work: Approximations and Metric Regularity in Mathematical Programming in Banach Space
cites work: Locally compactly Lipschitzian mappings in infinite dimensional programming
cites work: An Exact Penalization Viewpoint of Constrained Optimization
cites work: On the variational principle
cites work: Q3329946
cites work: Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear Systems
cites work: Q3869074
cites work: Q4104377
full work available at URL: https://doi.org/10.1007/bf02191853
OpenAlex ID: W1995063608
description: scientific article; zbMATH DE number 638719