Unconstrained optimization reformulations of equilibrium problems
The goal of the paper is to extend the D-gap function corresponding to variational inequalities to a general equilibrium problem (EP, for short). First, the EP is reformulated as an unconstrained optimization problem by using the proposed gap function. Then the authors give conditions to guarantee that the stationary point of the unconstrained optimization problem is a solution of EP. Finally, they show that the unconstrained optimization problem has a bounded level set and provide global error bounds for EP. In the introduction examples of reformulations of EP as variational inequalities are given and it is presented a literature review on the popular approach to solving variational inequalities as equivalent minimization problems.
scientific article; zbMATH DE number 5629505