Saturday, 14:20 - 16:00 - Room 161
Stream: Global optimization
The problem to find the adequate asymptotic function in the quasiconvex case is still an open problem in generalized convexity theory. But, What we mean with "adequate"?. In what sense?. In this talk, we focus on answering these questions, as a consequence, we develop properties for the q-asymptotic function defined for dealing with quasiconvex problems. We related this function with generalized derivatives and subdifferentials, also with the Fenchel-Moreau conjugacy and with a generalized support function. The formulas from the convex analysis are particular case of these new formulas.
Assume that for a large scale Global Optimization (GO) problem a set of features can be associated to each feasible solution. After running some time-consuming local searches of a randomized GO method, local optima are clustered in the selected features' space. Subsequent searches can then be stopped early when the current point is found to belong to a cluster, as it is likely that the resulting optimum will be very similar to one already discovered. An application to circle/disk packing proofs the validity of the approach. Many improved putative optima were discovered during the experiments.
Within the framework of abstract convexity we establish the links between the minimax equality for lower semicontinuous functions and the minimax equality for their convexification.
We provide relationships between sufficient condition for the minimax equality for abstract convex functions and constraint qualification conditions in optimization problems.
At first we consider the problem of maximizing the norm of a vector on the intersection of balls. This problem can be solved using dual method. Further, we consider general quadratic problem. This problem can be transformed in to the canonical form with positive and negative coefficients. We introduce new variables instead of quadratic variables. Further, we apply exact quadratic regularization. It transforms this problem into maximizing the norm of a vector on the intersection of balls with some prescribed tolerance. The numerical experiments have shown that new method is a very efficient.
Model inference is a challenging problem in the analysis of chemical reactions networks. In order to empirically test which model is governing a network of chemical reactions, it is fundamental to make an adequate choice of the control variables in order to have maximal separation between sets of concentrations provided by the theoretical models. In this work we illustrate how Global Optimization techniques can be used to address the problem of model separation, as a basis for model selection. Some examples illustrate the usefulness of our approach.