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Gap functions for quasi-variational inequalities via duality
1German-Mongolian Institute for Resources and Technology, Nalaikh, Mongolia.
Journal of Inequalities and Applications
|January 26, 2018
Summary
This study applies optimization duality theory to create gap functions for quasi-variational inequalities. This approach unifies previous findings on variational inequalities and equilibrium problems.
Area of Science:
- Optimization Theory
- Mathematical Analysis
Background:
- Duality theory is a powerful tool in optimization.
- Gap functions are essential for analyzing variational inequalities.
Purpose of the Study:
- To apply duality theory for constructing gap functions for quasi-variational inequalities.
- To extend previous research on variational inequalities and equilibrium problems.
Main Methods:
- Application of duality theory in optimization.
- Construction of gap functions.
Main Results:
- Successfully constructed gap functions for quasi-variational inequalities.
- Demonstrated that previous results for variational inequalities are special cases of this approach.
- Presented applications to generalized Nash equilibrium problems and mixed variational inequalities.
Conclusions:
- The proposed method effectively unifies and extends existing results in the field.
- Duality theory offers a robust framework for studying quasi-variational inequalities and related problems.
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