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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Vydáno v:Applied mathematics & optimization Ročník 40; číslo 2; s. 211 - 228
Hlavní autoři: Aizicovici, S., Pavel, D. Motreanu, N. H.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY Springer 01.09.1999
Témata:
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
Optimality condition
Wave operator
Non linear programming
Banach space
Optimal control (mathematics)
Linear operator
Partial differential equation
ISSN:0095-4616, 1432-0606
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Shrnutí: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.
ISSN:0095-4616
1432-0606
DOI:10.1007/s002459900123