Models and Methods of Semi-Infinite Optimization Inverse Heat-Conduction Problems

A broad range of inverse heat-conduction problems in their extreme statement, which are reduced to problems of optimum control by the corresponding system with distributed parameters, is analyzed. Parameterization of desired control actions by means of necessary extremum conditions is used for performing the procedure of accurate reduction to a special class of non-smooth finite-dimensional problems of mathematical programming, formulated in terms of the functions of a maximum. A computational algorithm for finding the solutions of these problems is proposed; this algorithm is based on alternance properties of the sought-for extremales, similar to analogous results in the theory of nonlinear Chebyshev approximations and on the a priori information on the characteristics of the analyzed functions of a maximum, dictated by the knowledge of the subject domain of the investigated problem. Possibilities of the proposed method are demonstrated by examples of solution of typical problems of optimum control, optimum design, and identification of thermophysical processes.