First- and second-order necessary conditions for control problems with constraints

Authors:
Zsolt Páles and Vera Zeidan

Journal:
Trans. Amer. Math. Soc. **346** (1994), 421-453

MSC:
Primary 49K15; Secondary 49J52

MathSciNet review:
1270667

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Abstract: Second-order necessary conditions are developed for an abstract nonsmooth control problem with mixed state-control equality and inequality constraints as well as a constraint of the form , where is a closed convex set of a Banach space with nonempty interior. The inequality constraints depend on a parameter belonging to a compact metric space . The equality constraints are split into two sets of equations and , where the first equation is an abstract control equation, and is assumed to have a full rank property in . The objective function is where is a compact metric space, is upper semicontinuous in and Lipschitz in . The results are in terms of a function that disappears when the parameter spaces and are discrete. We apply these results to control problems governed by ordinary differential equations and having pure state inequality constraints and control state equality and inequality constraints. Thus we obtain a generalization and extension of the existing results on this problem.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1270667-9

Keywords:
Nonsmooth functions,
second-order necessary conditions,
mixed state and/or control equality constraints,
state and/or control inequality constraints with parameter,
abstract control equation,
optimal controls

Article copyright:
© Copyright 1994
American Mathematical Society