非线性方程组解法在梯度投影约束最优化问题中的应用  

Application of nonlinear equation system solution ingradient projection constrained optimization problems

作　　者：王玮[1] WANG Wei(Zaozhuang Vocational College,Science and Technology,Zaozhuang Shandong 277500)

机构地区：[1]枣庄科技职业学院机械工程系,山东枣庄277500

出　　处：《宁夏师范学院学报》2020年第4期5-10,共6页Journal of Ningxia Normal University

摘　　要：为解决自适应学习算法的寻优能力较差的问题,分析非线性方程组解法在梯度投影约束最优化问题中的应用.首先,构建一类具有齐次特征解的非线性方程组解,采用双曲波动特征分析方法对非线性方程组解的最优化求解,建立非线性方程组解的最优解向量分析问题;然后,采用最大特征分解方法分析非线性方程组解的扰动性,并分析梯度投影约束最优化问题,结合梯度投影约束寻优方法对非线性方程组解空间拟合.最后,实现非线性方程组解法优化和梯度投影约束最优化.分析得知非线性方程组解法在梯度投影约束最优化寻优中具有收敛性和稳定性特征.该方法具有很好的特征优化能力.In order to solve the problem of poor optimization ability of adaptive learning algorithm,the application of nonlinear equations in gradient projection constrained optimization is analyzed.Firstly,a class of nonlinear equations with homogeneous characteristic solution is constructed,the hyperbolic wave characteristic analysis method is used to optimize the solution of the nonlinear equations,and the vector analysis problem of the optimal solution of the nonlinear equations is established.In addition,the maximum characteristic decomposition method is used to analyze the perturbation of the solution of the nonlinear equations,and the gradient projection constrained optimization problem is analyzed,combined with gradient.Finally,the optimization of nonlinear equations and gradient projection constraints are realized.It is found that the solution of nonlinear equations has the characteristics of convergence and stability in gradient projection constrained optimization.The proposed method has a good ability of feature optimization.

关 键 词：非线性方程组 梯度投影 约束 最优化问题 

分 类 号：O175.27[理学—数学]