一个求解退化二次规划问题的离散神经网络

发布时间：2018-05-04 06:31

本文选题：神经网络 + 退化二次规划　；参考：《西南大学》2017年硕士论文

【摘要】：二次优化问题在科学研究和工程应用中扮演着重要的角色,比如在还原分析、信号与图像处理、制造业、最优控制以及系统识别等方面都有重要应用。然而,传统的优化算法在实际应用中不容易硬件实现,且实时性能差。神经网络优化算法的出现克服了传统优化算法在硬件实现和实时处理两个方面的问题,这是因为:一方面,神经网络易于电路实现;另一方面,神经网络优化算法动态求解的过程是并行和分布式的,因此应用神经网络方法的运行时间远少于传统优化算法。退化二次优化在工程实践和生活实践中普遍存在,为解决此类问题,本文提出了一个离散时间神经网络优化算法,通过Lyapunov函数法验证了算法的稳定性,并通过实验仿真验证了算法的有效性。本文进一步将该算法应用于证券投资组合问题,得到了一定条件下最优的投资组合。论文的主要研究内容和创新点如下所述:1.提出了用于求解退化二次优化问题的离散时间神经网络优化算法。对一般的退化二次优化算法,先构造相应的拉格朗日函数,结合鞍点定理,利用投影的方法,找到对应的投影等式;再根据投影方程,提出了相应的离散时间神经网络模型;构造Lyapunov函数,验证了在给定条件下网络是全局收敛的。仿真结果表明该算法对于求解退化二次优化的有效性。2.利用提出的神经网络优化算法研究了一类最优投资组合问题。国内股票交易市场空前火爆,很多股民抗风险能力较差,因此在提高收益的同时降低风险就显得非常重要。通过分析Markowitz均值-方差模型,将最优投资组合的问题转化为二次规划问题,并用神经网络算法进行求解,最终找到了在给定收益的情况下,风险系数最小的投资组合。
[Abstract]:Quadratic optimization problems play an important role in scientific research and engineering applications, such as reduction analysis, signal and image processing, manufacturing, optimal control and system identification. However, the traditional optimization algorithm is not easy to implement in practical applications, and the real-time performance is poor. The emergence of neural network optimization algorithm overcomes the traditional optimization algorithm in hardware implementation and real-time processing, this is because: on the one hand, neural network is easy to achieve; on the other hand, The dynamic solving process of the neural network optimization algorithm is parallel and distributed, so the running time of the neural network method is much less than that of the traditional optimization algorithm. In order to solve this kind of problem, a discrete time neural network optimization algorithm is proposed in this paper. The stability of the algorithm is verified by Lyapunov function method. The effectiveness of the algorithm is verified by experimental simulation. In this paper, we apply the algorithm to the portfolio problem and obtain the optimal portfolio under certain conditions. The main contents and innovations of this paper are as follows: 1. A discrete time neural network optimization algorithm for degenerate quadratic optimization problems is proposed. For the general degenerate quadratic optimization algorithm, the corresponding Lagrange function is constructed first, and the corresponding projection equation is found by using the projection method combined with the saddle point theorem, and then the corresponding discrete-time neural network model is proposed according to the projection equation. The Lyapunov function is constructed to verify that the network is globally convergent under given conditions. Simulation results show that the algorithm is effective in solving degenerate quadratic optimization. A class of optimal portfolio problems is studied by using the proposed neural network optimization algorithm. The domestic stock market is extremely hot, and many investors have poor ability to resist risks, so it is very important to reduce the risk while increasing the return. By analyzing the Markowitz mean-variance model, the optimal portfolio problem is transformed into a quadratic programming problem and solved by a neural network algorithm. Finally, the portfolio with the smallest risk coefficient is found under the given income.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP183

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