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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >A Neurodynamic Optimization Approach to Bilevel Quadratic Programming
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A Neurodynamic Optimization Approach to Bilevel Quadratic Programming

机译：双层二次规划的神经动力学优化方法

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摘要

This paper presents a neurodynamic optimization approach to bilevel quadratic programming (BQP). Based on the Karush–Kuhn–Tucker (KKT) theorem, the BQP problem is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). It is proved that the global solution of the MPCC is the minimal one of the optimal solutions to multiple convex optimization subproblems. A recurrent neural network is developed for solving these convex optimization subproblems. From any initial state, the state of the proposed neural network is convergent to an equilibrium point of the neural network, which is just the optimal solution of the convex optimization subproblem. Compared with existing recurrent neural networks for BQP, the proposed neural network is guaranteed for delivering the exact optimal solutions to any convex BQP problems. Moreover, it is proved that the proposed neural network for bilevel linear programming is convergent to an equilibrium point in finite time. Finally, three numerical examples are elaborated to substantiate the efficacy of the proposed approach.
机译：本文提出了一种用于双层二次规划（BQP）的神经动力学优化方法。基于Karush–Kuhn–Tucker（KKT）定理，BQP问题简化为受互补性约束（MPCC）约束的一级数学程序。证明了MPCC的整体解是多重凸优化子问题的最优解的最小解。开发了递归神经网络来解决这些凸优化子问题。从任何初始状态开始，所提出的神经网络的状态都收敛到神经网络的平衡点，这只是凸优化子问题的最优解。与现有的针对BQP的递归神经网络相比，所提出的神经网络可以为任何凸BQP问题提供准确的最优解。此外，证明了所提出的用于双层线性规划的神经网络在有限时间内收敛到平衡点。最后，阐述了三个数值示例，以证实所提出方法的有效性。

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