Thursday, 13:15 - 13:40 h, Room: H 2053

 

Andrei Orlov
On an approach to special nonlinear bilevel problems

 

Abstract:
An investigation of bilevel programming problems (BPPs) in the view of elaboration of the efficient numerical methods is a challenge of contemporary theory and methods of mathematical optimization. We consider classes of BPPs where the upper level goal function is d.c. (represented by difference of two convex functions) or convex quadratic, and the lower level goal function is convex quadratic. Also we investigate BPPs with equilibrium at the lower level. The new approach to elaboration of optimistic solution methods for these classes of BPPs is proposed. The approach is based on a possibility of equivalent representation of BPPs as nonconvex optimization problems with the help of optimality condidions for the lower level problem. These nonconvex problems are solved by using the global search theory in d.c. optimization problems developed in our group for some classes of nonconvex optimization. The approach allows building efficient methods for finding global solutions in d.c. optimization problems. Computational testing of the elaborated methods has shown the efficiency of the approach. This work is carried out under financial support of RFBR (project no. 11-01-00270a).

 

Talk 1 of the contributed session Thu.2.H 2053
"Advances in global optimization II" [...]
Cluster 9
"Global optimization" [...]

 

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