solv.QP 要求 D 在 R 中是对称正定的

发布于 2024-09-15 02:39:59 字数 262 浏览 12 评论 0原文

当我对问题运行solve.QP时，我从R中得到以下错误：

Error in solve.QP(sigma, rep(0, 5), t(Amat), bvec, meq = 2) : 
  matrix D in quadratic function is not positive definite!

我的西格玛矩阵是对称的，但不是正定的。为什么需要这个？如果我自己使用拉格朗日函数解决它，我就能得到解决方案。那么R为什么要提出这样的要求呢？

原文

When I run solve.QP on my problem, I get the following error from R:

Error in solve.QP(sigma, rep(0, 5), t(Amat), bvec, meq = 2) : 
  matrix D in quadratic function is not positive definite!

My sigma matrix is symmetric but is not positive definite. Why is this needed? If I solve it myself using Lagrangian functions, I am able to get the solution. Then why is R imposing this requirement?

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小嗷兮 2024-09-22 02:39:59

Goldfarb-Idnani 算法首先计算
无约束解。因此，要求矩阵D
目标函数是正定的。

摘自 Fortran 源文件solve.QP.f：

c  this routine uses the Goldfarb/Idnani algorithm to solve the
c  following minimization problem:
c
c        minimize  -d^T x + 1/2 *  x^T D x
c        where   A1^T x  = b1
c                A2^T x >= b2
c
c  the matrix D is assumed to be positive definite.  Especially,
c  w.l.o.g. D is assumed to be symmetric.

The Goldfarb-Idnani algorithm starts off by calculating the
unconstrained solution. Thus, it requires that the matrix D in the
objective function is positive definite.

Excerpt from Fortran source file solve.QP.f:

c  this routine uses the Goldfarb/Idnani algorithm to solve the
c  following minimization problem:
c
c        minimize  -d^T x + 1/2 *  x^T D x
c        where   A1^T x  = b1
c                A2^T x >= b2
c
c  the matrix D is assumed to be positive definite.  Especially,
c  w.l.o.g. D is assumed to be symmetric.

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