## Annals of Functional Analysis

- Ann. Funct. Anal.
- Volume 6, Number 4 (2015), 107-113.

### Ekeland's variational principle and critical points of dynamical systems in locally complete spaces

C. Bosch, C.L. García, F. Garibay-Bonales, C. Gómez-Wulschner, and R. Vera

#### Abstract

Ekeland's variational principle and the existence of critical points of dynamical systems, also known as multiobjective optimization, have been proved in the setting of locally complete spaces. In this article we prove that these two properties can be deduced one from the other under certain convexity conditions.

#### Article information

**Source**

Ann. Funct. Anal. Volume 6, Number 4 (2015), 107-113.

**Dates**

First available in Project Euclid: 1 July 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.afa/1435764005

**Digital Object Identifier**

doi:10.15352/afa/06-4-107

**Mathematical Reviews number (MathSciNet)**

MR3365985

**Zentralblatt MATH identifier**

1326.49024

**Subjects**

Primary: 46N10: Applications in optimization, convex analysis, mathematical programming, economics

Secondary: 47N10: Applications in optimization, convex analysis, mathematical programming, economics 49J53: Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]

**Keywords**

Ekeland's variational principle locally complete space multiobjective optimization absolutely convex

#### Citation

Bosch, C.; García, C.L.; Garibay-Bonales, F.; Gómez-Wulschner, C.; Vera, R. Ekeland's variational principle and critical points of dynamical systems in locally complete spaces. Ann. Funct. Anal. 6 (2015), no. 4, 107--113. doi:10.15352/afa/06-4-107. https://projecteuclid.org/euclid.afa/1435764005