Strict lower subdifferentiability and applications

H. Xu, A. M. Rubinov, B. M. Glover
1999 The Journal of the Australian Mathematical Society Series B Applied Mathematics  
We investigate the strict lower subdifferentiability of a real-valued function on a closed convex subset of R". 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
more » ... ence results of the consequent algorithm are obtained.
doi:10.1017/s0334270000010961 fatcat:vlqwsvmtkfd7bimg4z5wqgccy4