Some algorithms for classes of split feasibility problems involving paramonotone equilibria and convex optimization

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...

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Bibliographic Details
Published in:Journal of inequalities and applications 2019-03, Vol.2019 (1), p.1-23, Article 77
Main Authors: Dong, Q. L., Li, X. H., Kitkuan, D., Cho, Y. J., Kumam, P.
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Applications of Mathematics
Computational geometry
Constrained convex optimization
Convergence
Convex analysis
Convexity
Economic models
Electricity pricing
Equilibria
Feasibility
Iterative methods
Mathematical models
Mathematics
Mathematics and Statistics
Optimization
Practical model
Split feasibility problem
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Summary: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.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-019-2030-x