朱莉娅错误使用带有diagind函数的凸包 [英] Julia error using convex package with diagind function

问题描述

我正在尝试解决问题

d = 0.5 * ||X - \Sigma||_{Frobenius Norm} + 0.01 * ||XX||_{1}, 

其中X是对称正定矩阵，所有诊断元素应为1.XX与X相同，除了对角矩阵为0.\ Sigma是已知的，我希望X的最小值为d.

where X is a symmetric positive definite matrix, and all the diagnoal element should be 1. XX is same with X except the diagonal matrix is 0. \Sigma is known, I want minimum d with X.

我的代码如下:

using Convex
m = 5;
A = randn(m, m); 
x = Semidefinite(5);
xx=x;
xx[diagind(xx)].=0;
obj=vecnorm(A-x,2)+sumabs(xx)*0.01;
pro= minimize(obj, [x >= 0]);
pro.constraints+=[x[diagind(x)].=1];
solve!(pro)

MethodError:没有与diagind(:: Convex.Variable)匹配的方法

MethodError: no method matching diagind(::Convex.Variable)

我只是通过约束矩阵中的对角线元素来解决最优问题，但似乎diagind函数在这里无法正常工作，我该如何解决问题.

I just solve the optimal problem by constrain the diagonal elements in matrix, but it seems diagind function could not work here, How can I solve the problem.

推荐答案

我认为以下内容可以满足您的需求:

I think the following does what you want:

m = 5
Σ = randn(m, m)
X = Semidefinite(m)
XX = X - diagm(diag(X))
obj = 0.5 * vecnorm(X - Σ, 2) + 0.01 * sum(abs(XX))
constraints = [X >= 0, diag(X) == 1]
pro = minimize(obj, constraints)
solve!(pro)

对于操作类型:

• diag 提取矩阵的对角线作为矢量
• diagm 从向量中构造对角矩阵

• diag extracts the diagonal of a matrix, as a vector
• diagm constructs a diagonal matrix out of a vector

因此，要使XX为对角线为零的X，我们从中减去X的对角线.为了约束具有对角线1的X，我们使用==将其对角线与1比较.

So, to have XX be X with zero diagonal, we subtract the diagonal of X from it. And to constrain X having diagonal 1, we compare its diagonal with 1, using ==.

一个好主意是尽可能保持不可变的值，而不是尝试修改事物.我不知道Convex是否支持.

It is a good idea to keep immutable values as far as possible, instead of trying to modify things. I don't know whether Convex even supports that.

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