An Invitation to Tame Optimization

The word “tame” is used in the title in the same context as in expressions like “convex optimization,” “nonsmooth optimization,” etc.—as a reference to the class of objects involved in the formulation of optimization problems. Definable and tame functions and mappings associated with various o-minimal structures (e.g. semilinear, semialgebraic, globally subanalytic, and others) have a number of remarkable properties which make them an attractive domain for various applications. This relates both to the power of results that can be obtained and the power of available analytic techniques. The paper surveys certain ideas and recent results, some new, which have been or (hopefully) can be productively used in studies relating to variational analysis and nonsmooth optimization.

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