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Strict lower subdifferentiability and applications

Published online by Cambridge University Press:  17 February 2009

H. Xu ,
A. M. Rubinov  and
B. M. Glover
H. Xu
Affiliation:
School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, Australia.
A. M. Rubinov
Affiliation:
School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, Australia.
B. M. Glover
Affiliation:
School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, Australia.
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Abstract

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We investigate the strict lower subdifferentiability of a real-valued function on a closed convex subset of Rn. Relations between the strict lower subdifferential, lower subdifferential, and the usual convex subdifferential are established. Furthermore, we present necessary and sufficient optimality conditions for a class of quasiconvex minimization problems in terms of lower and strict lower subdifferentials. Finally, a descent direction method is proposed and global convergence results of the consequent algorithm are obtained.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 3 , January 1999 , pp. 379 - 391
Copyright
Copyright © Australian Mathematical Society 1999

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