This presentation explores recent developments in the theory of duality and gap functions for equilibrium problems ([1,2,3,4]). We investigate the construction of gap functions derived from conjugate duality principles in convex optimization, providing a unified framework for analyzing equilibrium problems ([1]). The presentation concludes with a comprehensive review of recent literature and promising research directions, emphasizing potential applications in variational inequalities and Nash equilibrium problems. This work contributes to the broader understanding of duality theory in equilibrium problems and provides valuable tools for both theoretical analysis and practical implementations ([5]).

References

1. Altangerel, L., Bot, R. I. and Wanka, G. On Gap Functions for Equilibrium Problems via Fenchel Duality, Pacific Journal of Optimization 2 (3), 667-678, 2006.
2. Altangerel, L. On Gap Functions for Quasi-Equilibrium Problems Via Duality, Journal of Mathematical Sciences, 2024.
3. Konnov, I. V., Schaible, S. Duality for Equilibrium Problems under Generalized Monotonicity, Journal of Optimization Theory and Applications 104, 395-408.
4. Mastroeni, G. Gap functions for equilibrium problems, J. Glob. Optim. 27(4):411-426, 2003.
5. Pappalardo, M., Mastroeni, G. and Passacantando, M. Merit Functions: a Bridge Between Optimization and Equilibria, 4OR-Q J Oper Res 12, 1-33, 2014.