Abstract
We consider infinite-dimensional nonlinear programming problems which consist of minimizing a functionf 0(u) under a target set constraint. We obtain necessary conditions for minima that reduce to the Kuhn-Tucker conditions in the finite-dimensional case. Among other applications of these necessary conditions and related results, we derive Pontryagin’s maximum principle for a class of control systems described by semilinear equations in Hilbert space and study convergence properties of sequences of near-optimal controls for these systems.
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The work of this author was supported in part by the National Science Foundation under Grant DMS-8701877.
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Fattorini, H.O., Frankowska, H. Necessary conditions for infinite-dimensional control problems. Math. Control Signal Systems 4, 41–67 (1991). https://doi.org/10.1007/BF02551380
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DOI: https://doi.org/10.1007/BF02551380