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A homotopic method of studying multivalued problems. (English. Russian original) Zbl 0929.90076
Autom. Remote Control 57, No. 10, Pt. 2, 1513-1521 (1996); translation from Avtom. Telemekh. 1996, No. 10, 168-178 (1996).
Summary: A homotopy method of investigating optimization problems is discussed, in which the classes of functionals dependent on a parameter and having the following property: if the extremum of a functional is isolated in the course of deformation and if it is the minimum for some value of a parameter, then it is also the minimum of the corresponding functionals for all values of the parameter. This general principle finds wide application in classical problems, variational calculus, stability theory, mathematical physics, etc. In the past the deformation principle of minimum was extended to mathematical programming problems, nonsmooth optimization problems, and problems with nonisolated extrema. In this paper, the deformation principle of minimum is extended to multivalued problems in finite-dimensional space.
90C29 Multi-objective and goal programming