Date of Award

1995

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics and Statistics

First Advisor

Caron, R.

Keywords

Mathematics.

Rights

CC BY-NC-ND 4.0

Abstract

In this thesis we consider four problems arising from our study of quadratically constrained convex quadratic programmes (QCQP). The first problem concerns the representation of a quadratically constrained convex feasible region. We define the term "minimal representation" and give necessary and sufficient conditions for a representation to be minimal. The second problem deals with boundedness of quadratically constrained convex feasible regions. In particular, we provide necessary and sufficient conditions for unboundedness which are in the form of an algorithm which requires the identification of implicit equality constraints in homogeneous linear systems. The third problem is concerned with feasible regions which are either unbounded or not full dimensional; and with representations of these regions which may contain redundant constraints or pseudo-quadratic constraints. (A pseudo-quadratic constraint is a quadratic constraint that can be replaced with a finite number of linear inequality constraints). We show how a method of centers can be modified to solve problems with unbounded feasible regions, even in the case when no analytic center exists. We also give an algorithm to transform the problem into an equivalent problem which has a full dimensional feasible region in a lower dimensional space. Provided that an initial feasible point is given, the algorithm can also be used to find an initial interior point. Our methods of dealing with this third problem are unique in that they involve neither the addition of extra constraints nor the addition of extra variables. Finally we develop a new method for improving the rate of convergence of analytic center methods and of barrier function methods applied to QCQP. The underlying ideas lead to a superlinearly convergent predictor-corrector algorithm.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1995 .O28. Source: Dissertation Abstracts International, Volume: 56-11, Section: B, page: 6159. Adviser: Richard Caron. Thesis (Ph.D.)--University of Windsor (Canada), 1995.

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