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首页> 外文会议>The 8th international conference on optimization: Techniques and Applications >Solving Mathematical Programs with Equilibrium Constraints as Constrained Equations
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Solving Mathematical Programs with Equilibrium Constraints as Constrained Equations

机译：用平衡约束作为约束方程求解数学程序

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This paper aims at developing effective numerical methods for solving mathematical programs with equilibrium constraints. Due to the complementarity constraints, the usual constraint qualification such as the Mangasarian-Fromovitz constraint qualification does not hold at any feasible solution and there are various weaker stationary concepts such as C-/M-/S-stationarity (Clarke-/Mordukhovich-/Strong-stationarity) suggested in the literature. In this paper, we reformulate these stationary conditions as smooth equations with simple constraints. We then present a modified Levenberg-Marquardt method for solving these constrained equations. We show that, under some weak local error bound conditions, the method is locally and superlinearly convergent. Furthermore, we give some sufficient conditions for local error bounds to hold. We demonstrate by a number of examples to show that the conditions are not very stringent.
机译：本文旨在开发有效的数值方法来求解具有平衡约束的数学程序。由于互补性约束，通常的约束条件（例如，Mangasarian-Fromovitz约束条件）在任何可行的解决方案中均不成立，并且存在各种较弱的平稳概念，例如C- / M- / S-平稳性（Clarke- / Mordukhovich- /强平稳性）在文献中建议。在本文中，我们将这些平稳条件重新表述为具有简单约束的光滑方程。然后，我们提出了一种改进的Levenberg-Marquardt方法来求解这些约束方程。我们表明，在某些弱局部误差约束条件下，该方法是局部和超线性收敛的。此外，我们提供了一些足以保持局部误差范围的条件。我们通过许多示例来证明这些条件不是很严格。

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