# Nonlinear Programming Problems Associated with Closed Range Operators

## 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.

- Authors:

- Department of Mathematics, Ohio University, Athens, OH 45701 (United States)
- Department of Mathematics, University of Iasi, Ro-6600 Iasi (Romania)

- Publication Date:

- OSTI Identifier:
- 21067541

- Resource Type:
- Journal Article

- Journal Name:
- Applied Mathematics and Optimization

- Additional Journal Information:
- Journal Volume: 40; Journal Issue: 2; Other Information: DOI: 10.1007/s002459900123; Copyright (c) 1999 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 1999 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BANACH SPACE; MAPS; NONLINEAR PROBLEMS; NONLINEAR PROGRAMMING; OPTIMAL CONTROL; PARTIAL DIFFERENTIAL EQUATIONS

### Citation Formats

```
Aizicovici, S., Motreanu, D., and Pavel, N. H.
```*Nonlinear Programming Problems Associated with Closed Range Operators*. United States: N. p., 1999.
Web. doi:10.1007/S002459900123.

```
Aizicovici, S., Motreanu, D., & Pavel, N. H.
```*Nonlinear Programming Problems Associated with Closed Range Operators*. United States. doi:10.1007/S002459900123.

```
Aizicovici, S., Motreanu, D., and Pavel, N. H. Wed .
"Nonlinear Programming Problems Associated with Closed Range Operators". United States. doi:10.1007/S002459900123.
```

```
@article{osti_21067541,
```

title = {Nonlinear Programming Problems Associated with Closed Range Operators},

author = {Aizicovici, S. and Motreanu, D. and Pavel, N. H.},

abstractNote = {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.},

doi = {10.1007/S002459900123},

journal = {Applied Mathematics and Optimization},

issn = {0095-4616},

number = 2,

volume = 40,

place = {United States},

year = {1999},

month = {9}

}

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