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Analytic center cutting plane methods for variational inequalities over convex bodies
Renying Zeng1,2
11School of Mathematical Sciences, Chongqing Normal University, Chongqing, China.
Journal of Inequalities and Applications
|April 21, 2018
Summary
This study introduces new analytic center cutting plane methods for solving variational inequalities. These methods are designed for quasimonotone or pseudomonotone problems over convex domains.
Area of Science:
- Optimization Theory
- Numerical Analysis
Background:
- Variational inequalities are fundamental in optimization and game theory.
- Existing methods may face challenges with specific classes of inequalities or domain types.
Purpose of the Study:
- To develop novel analytic center cutting plane methods.
- To address quasimonotone and pseudomonotone variational inequalities.
- To handle both bounded and unbounded convex domains.
Main Methods:
- Iterative algorithms based on analytic center computations.
- Cutting plane techniques adapted for variational inequalities.
- Application to quasimonotone and pseudomonotone functions.
Main Results:
- Proposed analytic center cutting plane methods are effective for the targeted inequalities.
- The methods are applicable to a broader range of domain types.
Conclusions:
- The presented methods offer efficient solutions for specific variational inequality problems.
- This work extends the applicability of analytic center cutting plane algorithms.
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