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ps：线性规划，利用Matlab的优化工具进行求解。步骤：--- 1、手写：f、A、b、Aeq、b、ub、lb矩阵；--- 2、求解：[x,fval,exitflag,output] = linprog(f,A,b,Aeq,beq,lb,ub)例如： ...

ps:这是按照自己的理解写的程序，代码比较糙。献丑了，望海涵！#FR method'''min f(x) = 2x1^2+x2^2A = [[4,0],[0,2]]'''#original function#x is col vectorimport numpy as npdef func(x,A): return 0.5*(x.T@A@x)def fun...

ps:这是按照自己的理解写的程序，代码比较糙。献丑了，望海涵！#Gradient descent method'''min f(x) = 2x1^2+x2^2A = [[4,0],[0,2]]'''#x is col vectorimport numpy as npdef func(x,A): return 0.5*(x.T@A@x)def func_der(x...

ps:这是按照自己的理解写的程序，代码比较糙。献丑了，望海涵！#Successive Over Relaxation methodimport numpy as npimport sysdef SOR(x0,A,b,w): if A.shape[1] != x0.shape[0] and A.shape[0] != b.shape[0]: sys.e...

ps:这是按照自己的理解写的程序，代码比较糙。献丑了，望海涵！#GaussSeidelIteration interationimport numpy as npimport sysdef GaussSeidel(x0,A,b): if A.shape[1] != x0.shape[0] and A.shape[0] != b.shape[0]: s...

ps:这是按照自己的理解写的程序，代码比较糙。献丑了，望海涵！#Jacobi interationimport numpy as npimport sysdef Jacobi(x0,A,b): if A.shape[1] != x0.shape[0] and A.shape[0] != b.shape[0]: sys.exit('Please try...

Second-order cone program（二阶锥规划）标准形式：-A second-order cone program (SOCP) is an optimization problem of the form：#SOCPimport cvxpy as cpimport numpy as np#problem datamm,n,p,n_i = 3,10,5,5np...

Quadratic program（二次规划）标准形式：-A quadratic program is an optimization problem with a quadratic objective and affine equality and inequality constraints.import numpy as npimport cvxpy as cp#probl...

Least-squares（最小二乘）标准形式：-In a least-squares, or linear regression, problem, we have measurements and and seek a vector x∈Rn such that is close to . Closeness is defined as the sum of the squared...

PS：为了计算一个优化问题，特地去学习cvxpy库。确实好用，推荐大家!Linear program(线性规划)标准形式：-A linear program is an optimization problem with a linear objective and affine inequality constraints.#Example -Linear programimpo...

例1：解方程，并且求的导数fa = [8,0,0,0,0,0,17,0,-3,1];%降幂排列。每项的系数。xk = roots(fa);disp(xk);% 运行结果：% -0.9578 + 0.5907i% -0.9578 - 0.5907i% -0.0062 + 1.1577i% -0.0062 - 1.1577i% 0.9627 + 0.57...

本集的数值案例如下： Example 1: syms p x r solve(p*sin(x) == r) %chooses 'x' as the unknown and returns ans = asin(r/p) pi - asin(r/p) Example 2: ...

条件数的倒数：rcond(A)：A为矩阵，rcond(A)为A的1范数的条件数的倒数的 估计值。如果A的条件数越好，那么其值在1.0附近；反之，则在无穷小附近。%%矩阵的条件数A = [11,2,3,4; 7,-2,-3,-4; 0.1,0.2,0.3,0.5; 5,7,8,9];%1范数的条件数Ac1 = cond(A,1);%2范数的条件数Ac2 = c...

Tip：各种范数的定义。%%计算向量或者矩阵的一范数、二范数、无穷范数、p范数、F范数X = [1,-1,2,3] ;Y = [-0.5,89,0.06,-12]';A = [1,2,3,4;1,-2,-3,-4;0.1,0.2,0.3,0.5;5,7,8,9];%向量X的范数X1 = norm(X,1);X2 = norm(X);Xinf = norm(X,inf);%p...