# Regularization of Nonmonotone Variational Inequalities

## Abstract

In this paper we extend the Tikhonov-Browder regularization scheme from monotone to rather a general class of nonmonotone multivalued variational inequalities. We show that their convergence conditions hold for some classes of perfectly and nonperfectly competitive economic equilibrium problems.

- Authors:

- Department of Applied Mathematics, Kazan University, ul. Kremlevskaya 18, Kazan 420008 (Russian Federation), E-mail: Igor.Konnov@ksu.ru
- Department of Mathematics, Faculty of Education, Ain Shams University, Cairo (Egypt)
- Informatics Problems Institute of AS RT, Kazan 420012 (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21067421

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Applied Mathematics and Optimization; Journal Volume: 53; Journal Issue: 3; Other Information: DOI: 10.1007/s00245-005-0849-7; Copyright (c) 2006 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONVERGENCE; EQUILIBRIUM; VARIATIONAL METHODS

### Citation Formats

```
Konnov, Igor V., Ali, M.S.S., and Mazurkevich, E.O.
```*Regularization of Nonmonotone Variational Inequalities*. United States: N. p., 2006.
Web. doi:10.1007/S00245-005-0849-7.

```
Konnov, Igor V., Ali, M.S.S., & Mazurkevich, E.O.
```*Regularization of Nonmonotone Variational Inequalities*. United States. doi:10.1007/S00245-005-0849-7.

```
Konnov, Igor V., Ali, M.S.S., and Mazurkevich, E.O. Mon .
"Regularization of Nonmonotone Variational Inequalities". United States.
doi:10.1007/S00245-005-0849-7.
```

```
@article{osti_21067421,
```

title = {Regularization of Nonmonotone Variational Inequalities},

author = {Konnov, Igor V. and Ali, M.S.S. and Mazurkevich, E.O.},

abstractNote = {In this paper we extend the Tikhonov-Browder regularization scheme from monotone to rather a general class of nonmonotone multivalued variational inequalities. We show that their convergence conditions hold for some classes of perfectly and nonperfectly competitive economic equilibrium problems.},

doi = {10.1007/S00245-005-0849-7},

journal = {Applied Mathematics and Optimization},

number = 3,

volume = 53,

place = {United States},

year = {Mon May 15 00:00:00 EDT 2006},

month = {Mon May 15 00:00:00 EDT 2006}

}

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