# Optimization for the Sum of Finite Functions Over the Solution Set of Split Equality Optimization Problems with Applications

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## Abstract

In this paper, we adopt an iterative approach to solve the class of optimization problem for the sum of finite functions over split equality optimization problems for the sum of two functions. This type of problem contains many optimization problems, and bilevel problems, as well as split equality problems, and split feasibility problems as special cases. Here, we are able to establish a strong convergence theorem for an iterative method for solving this problem. As consequences of this convergence theorem, we study the following problems: optimization for the sum of finite functions over the common solution set of optimization problems for the sum of two functions; optimization for the sum of finite functions; optimization for the sum of finite functions with split equality inconsistent feasibility constraints; optimization for the sum of finite functions over the solution set for split equality constrained quadratic signal recovery problem; optimization for the sum of finite functions over the solution set of generalized split equality multiple set feasibility problem, and optimization for the sum of finite functions over the solution set of split equality linear equations problem. We use simultaneous iteration to establish strong convergence theorems for these problems. Our results generalize and improve many existing theorems for these types of problems in the literature and will have applications in nonlinear analysis, optimization problems and signal processing problems.

## Keywords

Optimization for the sum of finite functions Split equality optimization problem Split equality inconsistent feasibility problem Split equality quadratic signal recovery problem## Mathematics Subject Classification

47H06 47H09 47H10 47J25 65K15 90C35 90C25## Notes

### Acknowledgements

The author wishes to express his gratitude to the referees for their valuable suggestions during the preparation of this paper.

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