solve.QP require D to be symmetric positive definite in R

Question

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?

Answer 1

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.

solve.QP require D to be symmetric positive definite in R

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