On Penalty and Gap Function Methods for Bilevel Equilibrium Problems
Keyword(s):
We consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one-level ones. We generalize a pseudo-∇-monotonicity concept from∇-monotonicity and prove that under pseudo-∇-monotonicity property any stationary point of a regularized gap function is a solution of the penalized equilibrium problem. As an application, we discuss a special case that arises from the Tikhonov regularization method for pseudomonotone equilibrium problems.
2009 ◽
Vol 61
(8)
◽
pp. 1302-1310
◽
2017 ◽
Vol 26
(1)
◽
pp. 60-65
◽
2021 ◽
pp. 100246