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A system of nonlinear set valued variational inclusions
Yong-Kun Tang1, Shih-Sen Chang1, Salahuddin Salahuddin2
1College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221 China.
Springerplus
|August 1, 2014
Summary
This study introduces an iterative algorithm using the resolvent operator technique to solve complex nonlinear set valued variational inclusions in Hilbert spaces. The research proves the convergence of approximate solutions, offering new methods for this mathematical field.
Area of Science:
- * Mathematical Analysis
- * Nonlinear Analysis
- * Optimization Theory
Background:
- * Variational inclusion problems are fundamental in applied mathematics and optimization.
- * Existing methods face challenges with nonlinear, set-valued functions and specific mappings.
- * Hilbert spaces provide a robust framework for analyzing such complex mathematical structures.
Purpose of the Study:
- * To establish existence theorems for a system of nonlinear set valued variational inclusions.
- * To develop an iterative algorithm for approximating solutions to these complex systems.
- * To address challenges posed by proper convex lower semicontinuous functions and specific mappings.
Main Methods:
- * Utilized the resolvent operator technique, a powerful tool in nonlinear analysis.
- * Developed a novel iterative algorithm tailored for the specific structure of the inclusions.
- * Employed techniques from functional analysis within Hilbert spaces.
Main Results:
- * Successfully formulated an iterative algorithm to compute approximate solutions.
- * Proved the convergence of the iterative sequences generated by the algorithm.
- * Established existence theorems for the studied system of variational inclusions.
Conclusions:
- * The proposed resolvent operator technique and iterative algorithm are effective for solving nonlinear set valued variational inclusions.
- * The convergence proof validates the reliability of the computed approximate solutions.
- * This work contributes significant advancements to the theory and application of variational inclusions in Hilbert spaces.
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