Contributed Session Thu.2.H 2053

Thursday, 13:15 - 14:45 h, Room: H 2053

Cluster 9: Global optimization [...]

Advances in global optimization II


Chair: Alireza Doagooei



Thursday, 13:15 - 13:40 h, Room: H 2053, Talk 1

Andrei Vassilievich Orlov
On an approach to special nonlinear bilevel problems


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).



Thursday, 13:45 - 14:10 h, Room: H 2053, Talk 2

John Chinneck
Better placement of local solver launch points for global optimization

Coauthors: Victor Aitken, Laurence Smith


NLP solutions are quite sensitive to the launch point provided to the local solver, hence multi-start methods are needed if the global optimum is to be found. The drawback is that local solver launches are expensive. We limit the number of local solver launches by first using very fast approximate methods to explore the variable space to find a small number of promising locations for the local solver launches. We start with a set of random initial points, and then apply the Constraint Consensus (CC) method to quickly move to points that are close to feasibility. Clusters of the CC output points are then automatically identified; these generally correspond to disjoint feasible regions. Finally, the local solver is launched just once from each cluster, greatly improving efficiency. We frequently find a very good solution (if not the optimum solution) with very few local solver launches, and hence in relatively little time. Extensive empirical results are given.



Thursday, 14:15 - 14:40 h, Room: H 2053, Talk 3

Alireza Doagooei
Global optimization on the difference of sub-topical functions


We present the necessary and sufficient conditions for the global minimum of the difference of strictly sub-topical functions. Also, we will use the Toland-Singer formula to characterize the dual problem. Our main theoretical tool is abstract convexity.


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