quadratic programming best approximation dykstra algorithm ellipsoid method
Abstract:
This thesis regards the study of an efficient implementation of the method of alternating projections to semi-definite quadratic programming problems. Quadratic programming problems are ubiquitous. In canonical form they correspond to minimization of a quadratic form subject to linear inequality constraints. When the form is positive definite, a solution to the quadratic programming problem gives the closest point from a polyhedral set to a given point in space. Such solutions can also be used to approximate minimizers of nonlinear functions subject to nonlinear constraints. Our research focuses on Dykstra’s cyclic projections method. We implemented the Dykstra’s algorithm and compared the efficiency of Dykstra's algorithm with ellipsoid method.
