Geodesic
New global optimality conditions in a problem with d.c. constraints
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 1, pp. 245-261

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper addresses a nonconvex nonsmooth optimization problem with the cost function and equality and inequality constraints given by d.c. functions, i.e., functions representable as the difference of convex functions. The original problem is reduced to a problem without constraints with the help of exact penalization theory. Then the penalized problem is represented as a d.c. minimization problem without constraints, for which new mathematical tools are developed in the form of global optimality conditions (GOCs). The GOCs reduce the nonconvex problem in question to a family of linearized (convex) problems and are used to derive a nonsmooth form of the Karush-Kuhn-Tucker theorem for the original problem. In addition, the GOCs possess a constructive (algorithmic) property, which makes it possible to leave the local pits and stationary (critical) points of the original problem. The effectiveness of the GOCs is demonstrated with examples.
Keywords: d.c. function, exact penalty, linearized problem, global optimality conditions, Lagrange function, KKT-vector.
Mots-clés : Lagrange multipliers 
@article{TIMM_2019_25_1_a18,
     author = {A. S. Strekalovskii},
     title = {New global optimality conditions in a problem with d.c. constraints},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {245--261},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2019_25_1_a18/}
}
TY  - JOUR
AU  - A. S. Strekalovskii
TI  - New global optimality conditions in a problem with d.c. constraints
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2019
SP  - 245
EP  - 261
VL  - 25
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2019_25_1_a18/
LA  - ru
ID  - TIMM_2019_25_1_a18
ER  - 
%0 Journal Article
%A A. S. Strekalovskii
%T New global optimality conditions in a problem with d.c. constraints
%J Trudy Instituta matematiki i mehaniki
%D 2019
%P 245-261
%V 25
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2019_25_1_a18/
%G ru
%F TIMM_2019_25_1_a18
A. S. Strekalovskii. New global optimality conditions in a problem with d.c. constraints. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 1, pp. 245-261. http://geodesic.mathdoc.fr/item/TIMM_2019_25_1_a18/