A path following algorithm for infinite quadratic programming on a Hilbert space

Pages: 653 - 670, Volume 4, Issue 4, October 1998

doi:10.3934/dcds.1998.4.653       Abstract        Full Text (219.2K)       Related Articles

Andrew E.B. Lim - Department of Electrical & Electronic Engineering, University of Melbourne, Parkville Victoria 3052, Australia (email)
John B. Moore - Department of Systems Engineering, Australian National University, Canberra A.C.T. 0200, Australia (email)

Abstract: In this paper, we consider a path following algorithm for solving infinite quadratic programming problems. The convergence properties of a smoothly parametrized curve, known as the central trajectory, is studied. We show that the points of this curve converge to the optimal solution of the problem, so by approximating this curve, solutions arbitrarily close to the optimal solution can be calculated. As an example, we consider the linear-quadratic optimal control problem with state inequality constraints at every time instant.

Keywords:  Optimization, mathematical programming, interior point methods, infinite quadratic programming, constrained optimal control.
Mathematics Subject Classification:  65K, 90C.

Received: February 1997;      Revised: December 1997;      Published: July 1998.