Convex composite non–Lipschitz programming |
| |
Authors: | V Jeyakumar DT Luc PN Tinh |
| |
Institution: | (1) Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia, e-mail: jeya@maths.unsw.edu.au, AU;(2) Departement de Mathématiques, Université d’Avignon, 33 Rue Louis Pasteur, 8400 Avignon, France, e-mail: dtluc@univ-avignon.fr, FR;(3) Department of Mathematics, Faculty of Sciences, Hue University, Hue, Vietnam, VN |
| |
Abstract: | In this paper necessary, and sufficient optimality conditions are established without Lipschitz continuity for convex composite
continuous optimization model problems subject to inequality constraints. Necessary conditions for the special case of the
optimization model involving max-min constraints, which frequently arise in many engineering applications, are also given. Optimality conditions in the presence
of Lipschitz continuity are routinely obtained using chain rule formulas of the Clarke generalized Jacobian which is a bounded
set of matrices. However, the lack of derivative of a continuous map in the absence of Lipschitz continuity is often replaced
by a locally unbounded generalized Jacobian map for which the standard form of the chain rule formulas fails to hold. In this
paper we overcome this situation by constructing approximate Jacobians for the convex composite function involved in the model
problem using ε-perturbations of the subdifferential of the convex function and the flexible generalized calculus of unbounded
approximate Jacobians. Examples are discussed to illustrate the nature of the optimality conditions.
Received: February 2001 / Accepted: September 2001?Published online February 14, 2002 |
| |
Keywords: | : convex composite problems – unbounded approximate Jacobians – chain rules – optimality conditions – nonsmooth continuous maps Mathematics Subject Classification (1991): 90C45 |
本文献已被 SpringerLink 等数据库收录! |
|