𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On nonconvex optimization problems with separated nonconvex variables

✍ Scribed by Hoang Tuy

Publisher
Springer US
Year
1992
Tongue
English
Weight
628 KB
Volume
2
Category
Article
ISSN
0925-5001

No coin nor oath required. For personal study only.

✦ Synopsis

A mathematical programming problem is said to have separated nonconvex variables when the variables can be divided into two groups: x = (xl,..., x,) and y = (Yl,. β€’ β€’ , Yn), such that the objective function and any constraint function is a sum of a convex function of (x, y) jointly and a nonconvex function of x alone. A method is proposed for solving a class of such problems which includes Lipschitz optimization, reverse convex programming problems and also more general nonconvex optimization problems.

πŸ“œ SIMILAR VOLUMES

New dual-type decomposition algorithm fo
New dual-type decomposition algorithm for nonconvex separable optimization problems
✍ P. Tatjewski πŸ“‚ Article πŸ“… 1989 πŸ› Elsevier Science 🌐 English βš– 776 KB

Although the augmented Lagrange function is not separable, suitable reformulation of this function and introduction of auxiliary variables lead to a decomposition algorithm with simple and efficient adjusting rules for upper level variables.

Optimality conditions for a nonconvex se
Optimality conditions for a nonconvex set-valued optimization problem
✍ MarΓ­a Alonso; Luis RodrΓ­guez-MarΓ­n πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 253 KB

In this paper we study necessary and sufficient optimality conditions for a set-valued optimization problem. Convexity of the multifunction and the domain is not required. A definition of K -approximating multifunction is introduced. This multifunction is the differentiability notion applied to the