Approximation to optimization problems: an elementary review
Mathematics of Operations Research
Sample-path optimization of convex stochastic performance functions
Mathematical Programming: Series A and B
Sample-path solution of stochastic variational inequalities, with applications to option pricing
WSC '96 Proceedings of the 28th conference on Winter simulation
Analysis of sample-path optimization
Mathematics of Operations Research
A simulation-based approach to two-stage stochastic programming with recourse
Mathematical Programming: Series A and B
Proceedings of the 31st conference on Winter simulation: Simulation---a bridge to the future - Volume 1
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
Mathematics of Operations Research
The Sample Average Approximation Method for Stochastic Discrete Optimization
SIAM Journal on Optimization
Sensitivity Analysis for Stochastic User Equilibrium Network Flows-- A Dual Approach
Transportation Science
Solving stochastic mathematical programs with complementarity constraints using simulation
WSC '04 Proceedings of the 36th conference on Winter simulation
Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications)
Stochastic mathematical programs with equilibrium constraints
Operations Research Letters
Optimal Threshold Levels in Stochastic Fluid Models via Simulation-based Optimization
Discrete Event Dynamic Systems
Stochastic mathematical programs with hybrid equilibrium constraints
Journal of Computational and Applied Mathematics
Mathematics of Operations Research
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We consider stochastic mathematical programs with complementarity constraints in which both the objective and constraints involve limit functions that need to be approximated. Such programs can be used for modeling “average” (expected) or steady-state behavior of complex stochastic systems. We first describe these stochastic mathematical programs with complementarity constraints and compare them with different stochastic mathematical programs with equilibrium constraints from the literature. This explicit discussion may facilitate selecting an appropriate stochastic model. We then describe a simulation-based method called sample-path optimization for solving these problems and provide sufficient conditions under which appropriate approximating problems will have solutions converging to a solution of the original problem almost surely. We illustrate an application on toll pricing in transportation networks. We explain how uncertainty can be incorporated and the approximating problems are solved using an off-the-shelf solver. These developments enable solving certain stochastic bilevel optimization problems and Stackelberg games using simulation.