cvxpy中变量差异的范数

Question

如何在cvxpy

中采用以下规范

sum(norm(x[i] - x[j], p=2), i=1, j>i, i, j = n)

其中 x 是由 x = cp.Variable((n, 2)) 定义的 (n, 2) 变量矩阵。对于这个问题，我取 n=16。以下是我试图完全

的代码

import numpy as np
import cvxpy as cp


def solver(pts, var, lmb):
    objective = cp.Minimize(cp.norm(pts - var, 2) + cp.norm(var, 2))
    prob = cp.Problem(objective)
    prob.solve()
    print(prob.value)
    return np.round(var.value, 2)

pts = np.array([(-2, 3), (-3, 5), (-1, 4), (-3, 7) , (0, 3), 
                (-2, -2), (-3, 8), (3, 1), (1, -2), (2, 6), 
                (-2, 6), (-2, 5), (-4, 3), (-4, 6), (-3, 10), 
                (2, -3)])

n = pts.shape[0]
var = cp.Variable((n, 2))

solver(pts, var, 1)

Answer 1

正是因为你没有任何约束，你的问题就解决了。我跳过了使您的脚本更短的功能。

import numpy as np
import cvxpy as cp
pts = np.array([(-2, 3), (-3, 5), (-1, 4), (-3, 7), (0, 3),
                (-2, -2), (-3, 8), (3, 1), (1, -2), (2, 6),
                (-2, 6), (-2, 5), (-4, 3), (-4, 6), (-3, 10),
                (2, -3)])

n = pts.shape[0]
x = cp.Variable((n, 2))
objective = cp.Minimize(cp.sum(cp.norm(pts - x, 2, axis=1)))
prob = cp.Problem(objective)
prob.solve()

print(x.value)
# result
# [[-2.  3.]
#  [-3.  5.]
#  [-1.  4.]
#  [-3.  7.]
#  [ 0.  3.]
#  [-2. -2.]
#  [-3.  8.]
#  [ 3.  1.]
#  [ 1. -2.]
#  [ 2.  6.]
#  [-2.  6.]
#  [-2.  5.]
#  [-4.  3.]
#  [-4.  6.]
#  [-3. 10.]
#  [ 2. -3.]]

P.S。也许这不是您的正确答案。问题是从我在你的等式中看到的。我无法区分参数和您的值。

这是否意味着你有两个函数要最小化？一个接近点，另一个接近所有以前的点到当前点？

如果是这样，您可以将代码替换为：

cost1 = cp.sum(cp.norm(pts - x, 2, axis=1))
cost2 = cp.sum([cp.norm(x[j] - x[i],2) for i in range(1, n) for j in range(0, i)])
objective = cp.Minimize(cost1+cost2)
prob = cp.Problem(objective)
prob.solve()
print(x.value)
#result
# [[-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]
#  [-1.7909687  4.4720621]]

但是如您所见，结果并不那么有趣。

cvxpy中变量差异的范数

norm of differences of variables in cvxpy

python

cvxpy