基于微分中值定理的基本不等式证明方法

The Research of the Basic Inequality Proving Method Based on the Differential Mean Value Theorem

为了提高基本不等式的稳定解优化求解能力,提出基于微分中值定理的基本不等式证明方法,构建基本不等式的动态非均衡解向量约束模型,采用径向基函数参数化求导方法进行基本不等式证明的微分中值逼近运算。结合Volterra级数降阶方法实现基本不等式的结构化降维处理,提取基本不等式最优约束解的非线性特征量,采用形状可变结构的动力学评估方法,进行微分中值定理的优化构造,基于改进的微分中值定理进行基本不等式证明,结合Lyapunov稳定性原理,分析基本不等式证明方法的稳健性。研究得知,改进的基本不等式证明方法是稳健收敛的,满足条件一致性,对初始参数具有不敏感性,提高了基本不等式的输出稳态性。

In order to improve the ability of solving stable solutions of basic inequalities,a basic inequality proof method based on differential mean value theorem is proposed,and a vector constraint model of dynamic non-equilibrium solutions of basic inequalities is constructed.The radial basis function parameterized derivation method is used to calculate the differential median approximation of the basic inequality proof,and the structured dimensionality reduction of the basic inequality is realized by combining the Volterra series reduction method.The nonlinear characteristic quantity of optimal constrained solution of basic inequality is extracted,and the optimal construction of differential mean value theorem is carried out by using the dynamic evaluation method of variable shape structure,and the basic inequality is proved based on the improved differential mean value theorem.Based on the Lyapunov stability principle,the robustness of the basic inequality proof method is analyzed.It is found that the improved basic inequality proof method is robust convergence,satisfies the consistency of the conditions,is insensitive to the initial parameters,and improves the output stability of the basic inequality.