Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Growth behavior of a class of merit functions for the nonlinear complementarity problem
Journal of Optimization Theory and Applications
A class of smoothing functions for nonlinear and mixed complementarity problems
Computational Optimization and Applications
Some Noninterior Continuation Methods for LinearComplementarity Problems
SIAM Journal on Matrix Analysis and Applications
A stochastic version of a Stackelberg-Nash-Cournot equilibrium model
Management Science
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
Convergence analysis of stochastic algorithms
Mathematics of Operations Research
New NCP-functions and their properties
Journal of Optimization Theory and Applications
Error bounds in mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
On Homotopy-Smoothing Methods for Box-Constrained Variational Inequalities
SIAM Journal on Control and Optimization
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Properties of a Multivalued Mapping Associated with Some Nonmonotone Complementarity Problems
SIAM Journal on Control and Optimization
Smooth Approximations to Nonlinear Complementarity Problems
SIAM Journal on Optimization
Computers & Mathematics with Applications
Pricing American options with uncertain volatility through stochastic linear complementarity models
Computational Optimization and Applications
Recourse-based stochastic nonlinear programming: properties and Benders-SQP algorithms
Computational Optimization and Applications
The SC1 property of an expected residual function arising from stochastic complementarity problems
Operations Research Letters
Existence of optimal solutions for general stochastic linear complementarity problems
Operations Research Letters
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This paper presents a new formulation for the stochastic linear complementarity problem (SLCP), which aims at minimizing an expected residual defined by an NCP function. We generate observations by the quasi-Monte Carlo methods and prove that every accumulation point of minimizers of discrete approximation problems is a minimum expected residual solution of the SLCP. We show that a sufficient condition for the existence of a solution to the expected residual minimization (ERM) problem and its discrete approximations is that there is an observation ω i such that the coefficient matrix M(ω i) is an R0 matrix. Furthermore, we show that, for a class of problems with fixed coefficient matrices, the ERM problem becomes continuously differentiable and can be solved without using discrete approximation. Preliminary numerical results on a refinery production problem indicate that a solution of the new formulation is desirable.