Date of Award
Mathematics and Statistics
CC BY-NC-ND 4.0
In this thesis we are concerned with the behaviour of convex quadratic functions constrained by convex and concave quadratic constraints. In particular, we are concerned with the unboundedness of the functions over feasible regions defined by the constraints. For feasible regions defined only by convex constraints, or only by concave constraints, we present necessary and sufficient conditions for their unboundedness. We show that these conditions are equivalent to the existence of a feasible half line. We also present necessary and sufficient conditions for convex quadratic functions to be unbounded from above over the feasible regions, and to be unbounded from below over the feasible regions. For feasible regions defined by both convex and concave constraints we present sufficient conditions for their unboundedness. Similarly, we present sufficient conditions for convex quadratic functions to be unbounded from above over the feasible regions, and to be unbounded from below over the feasible regions. In all cases, we present numerical procedures for determining unboundedness. We also show that the implementation of the procedures only requires the solution of linear programmes having a very special structure.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1990 .O383. Source: Masters Abstracts International, Volume: 30-03, page: 0778. Adviser: Richard J. Caron. Thesis (M.Sc.)--University of Windsor (Canada), 1989.
Obuchowska, Wieslawa T., "Unboundedness of a quadratically constrained convex quadratic function." (1989). Electronic Theses and Dissertations. 4451.