Nonlinear Programming Problems Associated with Closed Range Operators

Nonlinear Programming Problems Associated with Closed Range Operators Necessary conditions for the optimality of a pair $(\overline{y}, \overline{u})$ with respect to a locally Lipschitz cost functional L(y,u) , subject to Ay + F(y) = Cu + B(u) , are given in terms of generalized gradients. Here A and C are densely defined, closed, linear operators on some Banach spaces, while F and B are (Fréchet) differentiable maps, which are suitably related to A and C . Various examples and potential applications to nonlinear programming models and nonlinear optimal control of partial differential equations are also discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Nonlinear Programming Problems Associated with Closed Range Operators

, Volume 40 (2) – Oct 1, 2074
18 pages

/lp/springer_journal/nonlinear-programming-problems-associated-with-closed-range-operators-uUqwB6qRsM
Publisher
Springer-Verlag
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002459900123
Publisher site
See Article on Publisher Site

Abstract

Necessary conditions for the optimality of a pair $(\overline{y}, \overline{u})$ with respect to a locally Lipschitz cost functional L(y,u) , subject to Ay + F(y) = Cu + B(u) , are given in terms of generalized gradients. Here A and C are densely defined, closed, linear operators on some Banach spaces, while F and B are (Fréchet) differentiable maps, which are suitably related to A and C . Various examples and potential applications to nonlinear programming models and nonlinear optimal control of partial differential equations are also discussed.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2074

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