2,262 research outputs found
Simulation-based solution of stochastic mathematical programs with complementarity constraints: Sample-path analysis
We consider a class of stochastic mathematical programs with complementarity constraints, in which both the objective and the constraints involve limit functions or expectations that need to be estimated or approximated. Such programs can be used for modeling \\average" or steady-state behavior of complex stochastic systems. Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models. Here we broaden the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints. The convergence analysis of sample-path methods rely heavily on stability conditions. We first review necessary sensitivity results, then describe the method, and provide sufficient conditions for its almost-sure convergence. Alongside we provide a complementary sensitivity result for the corresponding deterministic problems. In addition, we also provide a unifying discussion on alternative set of sufficient conditions, derive a complementary result regarding the analysis of stochastic variational inequalities, and prove the equivalence of two different regularity conditions.simulation;mathematical programs with equilibrium constraints;stability;regularity conditions;sample-path methods;stochastic mathematical programs with complementarity constraints
Simulation-Based Solution of Stochastic Mathematical Programs with Complementarity Constraints: Sample-Path Analysis
We consider a class of stochastic mathematical programs with complementarity constraints, in which both the objective and the constraints involve limit functions or expectations that need to be estimated or approximated.Such programs can be used for modeling average or steady-state behavior of complex stochastic systems.Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models.Here we broaden the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints.The convergence analysis of sample-path methods rely heavily on stability conditions.We first review necessary sensitivity results, then describe the method, and provide sufficient conditions for its almost-sure convergence.Alongside we provide a complementary sensitivity result for the corresponding deterministic problems.In addition, we also provide a unifying discussion on alternative set of sufficient conditions, derive a complementary result regarding the analysis of stochastic variational inequalities, and prove the equivalence of two different regularity conditions.stochastic processes;mathematics;stability;simulation;regulations;general equilibrium
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Entropic approximation for mathematical programs with robust equilibrium constraints
In this paper, we consider a class of mathematical programs with robust equilibrium constraints represented by a system of semi-infinite complementarity constraints (SIC C). We propose a numerical scheme for tackling SICC. Specific ally, by relaxing the complementarity constraints and then randomizing the index set of SICC, we employ the well-known entropic risk measure to approximate the semi-infinite onstraints with a finite number of stochastic inequality constraints. Under some moderate conditions, we quantify the approximation in term s of the feasible set and the optimal value. The approximation scheme is then applied to a class of two stage stochastic mathematical programs with complementarity constraints in combination with the polynomial decision rules. Finally, we extend the discussion to a mathematical program with distributionally robust equilibrium constraints which is essentially a one stage stochastic program with semi-infinite stochastic constraints indexed by some probability measures from an ambiguity set defined through the KL-divergence
Stochastic mathematical programs with hybrid equilibrium constraints
AbstractThis 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
Simulation-based solution of stochastic mathematical programs with complementarity constraints: Sample-path analysis
We consider a class of stochastic mathematical programs with complementarity constraints, in which both the objective and the constraints involve limit functions or expectations that need to be estimated or approximated. Such programs can be used for modeling \\average" or steady-state behavior of complex stochastic systems. Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models. Here we broaden the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints. The convergence analysis of sample-path methods rely heavily on stability conditions. We first review necessary sensitivity results, then describe the method, and provide sufficient conditions for its almost-sure convergence. Alongside we provide a complementary sensitivity result for the corresponding deterministic problems. In addition, we also provide a unifying discussion on alternative set of sufficient conditions, derive a complementary result regarding the analysis of stochastic variational inequalities, and prove the equivalence of two different regularity conditions
Modeling of Competition and Collaboration Networks under Uncertainty: Stochastic Programs with Resource and Bilevel
We analyze stochastic programming problems with recourse characterized by a bilevel structure. Part of the uncertainty in such problems is due to actions of other actors such that the considered decision maker needs to develop a model to estimate their response to his decisions. Often, the resulting model exhibits connecting constraints in the leaders (upper-level) subproblem. It is shown that this problem can be formulated as a new class of stochastic programming problems with equilibrium constraints (SMPEC). Sufficient optimality conditions are stated. A solution algorithm utilizing a stochastic quasi-gradient method is proposed, and its applicability extensively explained by practical numerical examples
Simulation-based solution of stochastic mathematical programs with complementarity constraints: sample-path analyis
We consider a class of stochastic mathematical programs with
complementarity constraints, in which both the objective and the
constraints involve limit functions or expectations that need to be
estimated or approximated. Such programs can be used for modeling
"average" or steady-state behavior of complex stochastic
systems. Recently, simulation-based methods have been successfully
used for solving challenging stochastic optimization problems and
equilibrium models. Here we broaden the applicability of so-called
the sample-path method to include the solution of certain stochastic
mathematical programs with equilibrium constraints. The convergence
analysis of sample-path methods rely heavily on stability
conditions. We first review necessary sensitivity results, then
describe the method, and provide sufficient conditions for its
almost-sure convergence. Alongside we provide a complementary
sensitivity result for the corresponding deterministic problems. In
addition, we also provide a unifying discussion on alternative set of
sufficient conditions, derive a complementary result regarding the
analysis of stochastic variational inequalities, and prove the
equivalence of two different regularity conditions
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