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Research on Smoothing Methods for Mathematical Programs with Equilibrium Constraints

Author: TanLing
Tutor: DuanFuJian
School: Guilin University of Electronic Science and Technology
Course: Applied Mathematics
Keywords: Equilibrium Constraints problem Complementarity Constraints Conjugate Projection Gradient Smooth SQP Global Convergence Superlinear convergence
CLC: O221
Type: Master's thesis
Year: 2009
Downloads: 40
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Abstract


Mathematical programming problems with equilibrium constraints (MPEC), also known as the equilibrium constraint optimization problems or balance problems, originated in economic issues, closely linked with the the famous stackelberg game theory, generalization of the theory of bi-level programming problem. problem has been widely applied in many other areas of engineering design, transportation, economic equilibrium, and multi-layer planning, has become one of the most active research topics in the field of international optimize its research in recent years more and more people's attention However, due to the existence of equilibrium constraints, resulting in a significant difference with the general nonlinear programming (NLP), standard nonlinear programming (NLP) Constraint specification in MPEC feasible domain no longer valid. thus as a In this paper, the standard nonlinear programming (NLP) Optimal conditions and algorithm theory can not be used to solve problems with equilibrium constraints, which is solving Equilibrium Constraints greatest difficulty and complexity of the algorithm underlying causes. the following three aspects: first, with perturbed the FB complementary functions and the semi-penalty function, the linear equalizer constrained optimization problem into a general constraint programming problem. Conjugate projection technology and the idea of ??the SQP method, a conjugate gradient projection algorithm that does not require solving quadratic programming sub-problems, and also to avoid the calculation of the generalized projection-type auxiliary direction, each iteration only need to calculate an explicit main search direction and to overcome the the Maratos effect of requirements automatically generated explicit correction direction, so as to further simplify the structure of the algorithm and the computational workload. algorithm has global convergence and superlinear convergence is proved under appropriate assumptions. followed by polishing technology, the non-linear equilibrium constraints in solving the optimization problem into sense equivalent to the original problem smooth, gradually approaching the idea, put forward a smooth approximation SQP algorithm at each iteration, calculated by solving a linear constrained quadratic programming problems and explicit correction direction of the main direction, significant -formulas to get the direction of the higher-order correction to avoid the Maratos effect. algorithm is proved under the assumption without any upper complementary global convergence and strong convergence and superlinear convergence speed. Finally, two articles The algorithms are numerical experiments, experimental results show that the algorithm is effective and feasible.

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Planning Theory ( mathematical programming)
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