Regularized Minimization of Convex Functions in Radon Nikodym Space

Regularized Minimization of Convex Functions in Radon Nikodym Space

Volume 4, Issue 2, Article 2 - 2018

Authors: Nourddin SAIDOU;Mhamed ZINEDDINE; Bouchaib Ferrahi

Copyright © 2018 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract

Convex non linear optimization problems may not have a solution in innite dimension spaces. The aim of this paper is to formulate some new results in this topic by using "technical regularization" of the objective function. The rst result shows that a non linear convex proper lower semi-continuous function, on a Banach space which have the Radon-Nikodym property, could be minimized by using a small regularization. while the second one shows that this regularization can be chosen as small as required. In addition, application tracks are presented and illustrated by elementary examples.

How To Cite This Article

@article{SAIDOU_2018, doi = {10.31559/glm2016.4.2.2}, url = {https://doi.org/10.31559%2Fglm2016.4.2.2}, year = 2018, month = {apr}, publisher = {Refaad for Studies and Research}, volume = {4}, number = {2}, pages = {61--66}, author = {Nourddin SAIDOU and and Mhamed ZINEDDINE and Bouchaib Ferrahi}, title = {Regularized Minimization of Convex Functions in Radon Nikodym Space}, journal = {General Letters in Mathematics} }
SAIDOU, N., ZINEDDINE, M., & Ferrahi, B. (2018). Regularized Minimization of Convex Functions in Radon Nikodym Space. General Letters in Mathematics, 4(2), 61–66. doi:10.31559/glm2016.4.2.2
[1]N. SAIDOU, M. ZINEDDINE, and B. Ferrahi, “Regularized Minimization of Convex Functions in Radon Nikodym Space,” General Letters in Mathematics, vol. 4, no. 2, pp. 61–66, Apr. 2018.
SAIDOU, Nourddin, Mhamed ZINEDDINE, and Bouchaib Ferrahi. “Regularized Minimization of Convex Functions in Radon Nikodym Space.” General Letters in Mathematics 4, no. 2 (April 1, 2018): 61–66. doi:10.31559/glm2016.4.2.2.