Convergence analysis of an iterative algorithm for the extended regularized nonconvex variational inequalities.
Ying Zhao1, Luoyi Shi1, Rudong Chen1
1Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387 P.R. China.
Journal of Inequalities and Applications
|May 13, 2017
Summary
This study introduces a new system for extended regularized nonconvex variational inequalities, proving its equivalence to a fixed point problem. A novel iterative algorithm is presented for solving these inequalities, with convergence analysis provided.
Area of Science:
- Optimization Theory
- Nonconvex Analysis
- Mathematical Programming
Background:
- Variational inequalities are fundamental in modeling various problems in applied mathematics and economics.
- Nonconvexity and regularization introduce complexities in solving these inequality systems.
- Equivalence to fixed point problems offers alternative solution strategies.
Purpose of the Study:
- To propose and analyze a new system of extended regularized nonconvex variational inequalities.
- To establish the equivalence between this system and a fixed point problem.
- To develop and analyze a novel iterative algorithm for solving the proposed system.
Main Methods:
- Formulation of a new system of extended regularized nonconvex variational inequalities.
- Proof of equivalence between the variational inequality system and a fixed point problem.
- Development of a perturbed projection iterative algorithm with mixed errors.
Main Results:
- The proposed system is shown to be equivalent to a fixed point problem.
- A new perturbed projection iterative algorithm is introduced.
- Convergence analysis of the iterative algorithm is established under moderate assumptions.
Conclusions:
- The study successfully formulates and analyzes a new class of variational inequalities.
- The developed iterative algorithm provides an effective method for solving these complex problems.
- The convergence properties ensure the reliability of the proposed solution method.
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