On weighted linear least-squares problems related to interior
methods for convex quadratic programming
Anders Forsgren and Göran Sporre
It is known that the norm of the solution to a weighted linear
least-squares problem is uniformly bounded for the set of diagonally
dominant symmetric positive definite weight matrices. This result is
extended to weight matrices that are nonnegative linear combinations
of symmetric positive semidefinite matrices. Further, results are
given concerning the strong connection between the boundedness of
weighted projection onto a subspace and the projection onto its
complementary subspace using the inverse weight matrix. In particular,
explicit bounds are given for the Euclidean norm of the projections.
We apply these results to the Newton equations arising in a
primal-dual interior method for convex quadratic programming and prove
boundedness for the corresponding projection operator.
Report TRITA-MAT-2000-OS11, Department of Mathematics,
Royal Institute of Technology, Stockholm, Sweden, 2000.