Stabilization method for unstable equilibrium programming problems with coupled constraints. (Q1874991)

The following equilibrium programming problem with coupled constraints is given: Find a point \(v_ *\) satisfying the conditions \[ v_ *\in V(v_ *),\qquad \Phi(v_ *,v_ *)\leq\Phi(v_ *,w)\quad \forall w\in V(v_ *), \] where \[ V(v)=\{w\in W_ 0\;| \; g_ i(v,w)\leq 0,\;i=1,\dots,m\},\quad W_ 0\subseteq E^ n. \] It is assumed that instead of the exact functions \(\Phi,g_ i\) their approximations \(\Phi_ {\delta},g_ {i\delta}\), which depend on an error parameter \(\delta > 0\), are known. Using a penalty function and a stabilizer of the given problem we introduce a stabilization method and prove that the method converges under certain conditions.