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SIAM J. CONTROL OPTIM. c 2005 Society for Industrial and Applied Mathematics Vol. 44, No. 5, pp. 17661786
 

Summary: SIAM J. CONTROL OPTIM. c 2005 Society for Industrial and Applied Mathematics
Vol. 44, No. 5, pp. 1766­1786
INTERIOR POINT METHODS IN FUNCTION SPACE
MARTIN WEISER
Abstract. A primal-dual interior point method for optimal control problems is considered.
The algorithm is directly applied to the infinite-dimensional problem. Existence and convergence
of the central path are analyzed, and linear convergence of a short-step path-following method is
established.
Key words. interior point methods in function space, optimal control, complementarity func-
tions
AMS subject classifications. 49M15, 90C48, 90C51
DOI. 10.1137/S0363012903437277
1. Introduction. Numerical methods for solving optimal control problems gov-
erned by ODEs fall into two categories, the indirect methods [2, 3, 4, 6, 14, 15, 31]
relying on Pontryagin's maximum principle, and the direct methods [7, 17, 21, 30, 37]
based on the Karush­Kuhn­Tucker necessary conditions. Direct methods can be
characterized by several features. Among them are the following:
(i) Position of discretization: Discretize-then-optimize approaches use an a priori
parameterization of the control and possibly the state variables to reduce the
optimal control problem to a finite-dimensional nonlinear program. These

  

Source: Andrzejak, Artur - Konrad-Zuse-Zentrum für Informationstechnik Berlin

 

Collections: Computer Technologies and Information Sciences