Stochastic mathematical programs with hybrid equilibrium constraints

This paper considers a stochastic mathematical program with hybrid equilibrium constraints (SMPHEC), which includes either ‘here‐and‐now’ or ‘wait‐and‐see’ type complementarity constraints. An example is given to describe the necessity to study SMPHEC. In order to solve the problem, the sampling average approximation techniques are employed to approximate the expectations and smoothing and penalty techniques are used to deal with the complementarity constraints. Limiting behaviors of the proposed approach are discussed. Preliminary numerical experiments show that the proposed approach is applicable.