Output details

Necessary Optimality Conditions for two-stage Stochastic Programs with Equilibrium Constraints

Stochastic mathematical programs with equilibrium constraints (SMPEC) is a new class of stochastic optimization problems which differs from the classical models by including equilibrium constraints which allow one to capture competition or structural balance in many decision making problems and engineering design. This paper addresses a key theoretical issue for two stage SMPECs: characterizing optimality through first order derivatives of the underlying functions, which is known as Karush-Kuhn-Tucker conditions. A theoretical breakthrough has been made on exchange rule for the Mordukhovich’s limiting subdifferential operator with the mathematical expectation operator for Lipschitz functions.