Characterizing robust weak sharp solution sets of convex optimization problems with uncertainty

Jutamas Kerdkaew; Rabian Wangkeeree

doi:10.3934/jimo.2019074

Article Contents

2020, Volume 16, Issue 6: 2651-2673. Doi: 10.3934/jimo.2019074

This issue Previous Article Admission control for finite capacity queueing model with general retrial times and state-dependent rates Next Article An adaptively regularized sequential quadratic programming method for equality constrained optimization

Characterizing robust weak sharp solution sets of convex optimization problems with uncertainty

Jutamas Kerdkaew^1, and
Rabian Wangkeeree^1,2, ,

1.
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2.
Research center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok 65000, Thailand

^* Corresponding author: R. Wangkeeree
^* Corresponding author: R. Wangkeeree

Received: February 28, 2018

Revised: February 28, 2019

Early access: July 2019

Published: October 2020

The first author was partially supported by the Science Achivement Scholarship of Thailand and the second author was partially supported by the Thailand Research Fund, Grant No. RSA6080077 and Naresuan University

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Abstract

We introduce robust weak sharp and robust sharp solution to a convex programming with the objective and constraint functions involved uncertainty. The characterizations of the sets of all the robust weak sharp solutions are obtained by means of subdiferentials of convex functions, DC fuctions, Fermat rule and the robust-type subdifferential constraint qualification, which was introduced in X.K. Sun, Z.Y. Peng and X. Le Guo, Some characterizations of robust optimal solutions for uncertain convex optimization problems, Optim Lett. 10. (2016), 1463-1478. In addition, some applications to the multi-objective case are presented.

Keywords:

Robust weak sharp solutions,
subdifferential,
uncertain convex optimization,
weakly Robust weak sharp efficient solutions.

Mathematics Subject Classification: Primary: 90C25, 90C46, 90C29; Secondary: 90C30.

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References

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