Some algorithms for classes of split feasibility problems involving paramonotone equilibria and convex optimization
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Publication Details
Author list: Dong Q.L., Li X.H., Kitkuan D., Cho Y.J., Kumam P.
Publisher: SpringerOpen
Publication year: 2019
Journal: Journal of Inequalities and Applications (1025-5834)
Volume number: 2019
Issue number: 1
ISSN: 1025-5834
eISSN: 1029-242X
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we first introduce a new algorithm which involves projecting each iteration to solve a split feasibility problem with paramonotone equilibria and using unconstrained convex optimization. The strong convergence of the proposed algorithm is presented. Second, we also revisit this split feasibility problem and replace the unconstrained convex optimization by a constrained convex optimization. We introduce some algorithms for two different types of objective function of the constrained convex optimization and prove some strong convergence results of the proposed algorithms. Third, we apply our algorithms for finding an equilibrium point with minimal environmental cost for a model in electricity production. Finally, we give some numerical results to illustrate the effectiveness and advantages of the proposed algorithms. ฉ The Author(s) 2019.
Keywords
Constrained convex optimization, Equilibria, Practical model
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