# American Institute of Mathematical Sciences

October  1998, 4(4): 653-670. doi: 10.3934/dcds.1998.4.653

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

 1 Department of Electrical & Electronic Engineering, University of Melbourne, Parkville Victoria 3052, Australia 2 Department of Systems Engineering, Australian National University, Canberra A.C.T. 0200, Australia

Received  February 1997 Revised  December 1997 Published  July 1998

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.
Citation: Andrew E.B. Lim, John B. Moore. A path following algorithm for infinite quadratic programming on a Hilbert space. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 653-670. doi: 10.3934/dcds.1998.4.653
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