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Discontinuity, Nonlinearity, and Complexity 9(4) (2020) 553--558 | DOI:10.5890/DNC.2020.12.008

R. Sengupta$^{1}$ , S. Zhukovskiy$^{2}$

$^1$ Faculty of Science, Peoples' Friendship University of Russia, 117198, Moscow, Mikluho-Maklaya st., 6

$^2$ V. A. Trapeznikov Institute of Control Sciences of RAS,117997, Moscow, Profsoyuznaya st., 65

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Abstract

A modification of the Ekeland variational principle for functions unbounded from below is obtained. For a wide class of differentiable functions not necessarily bounded below, it is shown that there exists a minimizing sequence satisfying the first-order necessary conditions, up to any desired approximation.

Acknowledgments

The research is supported by the Volkswagen Foundation and the Russian Foundation for Basic Research (Projects No 20-31-70013, 19-01-00080). The results in Section 3 are due to the second author who was supported by the Russian Science Foundation (Project No 20-11-20131).

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