Stability of the solution of definite quadratic programs

This paper studies how the solution of the problem of minimizingQ(x) = 1/2x ^T Kx – k ^T x subject toGx g andDx = d behaves whenK, k, G, g, D andd are perturbed, say by terms of size, assuming thatK is positive definite. It is shown that in general the solution moves by roughly ifG, g, D andd are not perturbed; whenG, g, D andd are in fact perturbed, much stronger hypotheses allow one to show that the solution moves by roughly. Many of these results can be extended to more general, nonquadratic, functionals.This research was supported in part by contract number N00014-67-A-0126-0015, NR 044-425 from the Office of Naval Research.