求解线性组合的算法? [英] Algorithm for Solving a Linear Combination?

问题描述

在我正在从事的项目中，我遇到了以下需要解决的问题:

I have run into the following problem that I need to solve in a project that I'm working on:

给出一定数量的向量v_i(在数学意义上)和目标向量H，计算与目标向量H最接近的向量v_i的线性组合，其约束条件是系数必须在[0 ，1].

Given some number of vectors v_i (in the math sense), and a target vector H, compute a linear combination of the vectors v_i that most closely matches the target vector H, with the constraint that the coefficients must be in [0, 1].

我不太了解应该使用哪种算法/数学方法来解决此类问题.任何朝着正确方向前进的产品将不胜感激！

I do not know much about what kind of algorithms / math should be used to approach such a problem. Any prods in the right general direction would be much appreciated!

推荐答案

这是一个受约束的最小二乘问题.基本上，您想解决优化问题:

It's a constrained least square problem. Basically you want to solve the optimization problem:

  argmin ||Ax-H||
    x
  s.t.  0<=x_j<=1

其中x=(x_1, ..., x_j, ..., x_n)包含要查找的系数，A的列对应于向量v_i.

where x=(x_1, ..., x_j, ..., x_n) consists the coefficients you are seeking, and a column of A corresponds to a vector v_i.

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