Continuous minimax optimization using modal intervals

AbstractMany real life problems can be stated as a continuous minimax optimization problem. Well-known applications to engineering, finance, optics and other fields demonstrate the importance of having reliable methods to tackle continuous minimax problems. In this paper a new approach to the solution of continuous minimax problems over reals is introduced, using tools based on modal intervals. Continuous minimax problems, and global optimization as a particular case, are stated as the computation of semantic extensions of continuous functions, one of the key concepts of modal intervals. Modal intervals techniques allow to compute, in a guaranteed way, such semantic extensions by means of an efficient algorithm. Several examples illustrate the behavior of the algorithms in unconstrained and constrained minimax problems

Reliable Minimax Parameter Estimation

This paper deals with the minimax parameter estimation of nonlinear parametric models from experimental data. Taking advantage of the special structure of the minimax problem, a new efficient and reliable algorithm based on interval constraint propagation is proposed. As an illustration, the ill-conditioned problem of estimating the parameters of a two-exponential model is considered