Nonlinear Programming Problems Associated with Closed Range Operators
Necessary conditions for the optimality of a pair (y-bar, u-bar) 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...
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| Veröffentlicht in: | Applied mathematics & optimization Jg. 40; H. 2; S. 211 - 228 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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New York, NY
Springer
01.09.1999
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| ISSN: | 0095-4616, 1432-0606 |
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| Abstract | Necessary conditions for the optimality of a pair (y-bar, u-bar) 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 (Frechet) 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. |
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| AbstractList | Necessary conditions for the optimality of a pair (y-bar, u-bar) 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 (Frechet) 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. |
| Author | Aizicovici, S. Pavel, D. Motreanu, N. H. |
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| Issue | 2 |
| Keywords | Optimality condition Wave operator Non linear programming Banach space Optimal control (mathematics) Linear operator Partial differential equation |
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| SubjectTerms | Applied sciences BANACH SPACE CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Exact sciences and technology Mathematical programming Mathematics NONLINEAR PROBLEMS NONLINEAR PROGRAMMING Numerical analysis Numerical analysis. Scientific computation Operational research and scientific management Operational research. Management science OPTIMAL CONTROL Ordinary differential equations PARTIAL DIFFERENTIAL EQUATIONS Sciences and techniques of general use |
| Title | Nonlinear Programming Problems Associated with Closed Range Operators |
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