On largescale nonlinear programming techniques for solving optimal control problems
Abstract
The formulation of decision problems by Optimal Control Theory allows the consideration of their dynamic structure and parameters estimation. This paper deals with techniques for choosing directions in the iterative solution of discretetime optimal control problems. A unified formulation incorporates nonlinear performance criteria and dynamic equations, time delays, bounded state and control variables, free planning horizon and variable initial state vector. In general they are characterized by a large number of variables, mostly when arising from discretization of continuoustime optimal control or calculus of variations problems. In a GRG context the staircase structure of the jacobian matrix of the dynamic equations is exploited in the choice of basic and super basic variables and when changes of basis occur along the process. The search directions of the bound constrained nonlinear programming problem in the reduced space of the super basic variables are computed by largescale NLP techniques. A modified PolakRibiere conjugate gradient method and a limited storage quasiNewton BFGS method are analyzed and modifications to deal with the bounds on the variables are suggested based on projected gradient devices with specific linesearches. Some practical models are presented for electric generation planning and fishery management, and the application of the code GRECOmore »
 Authors:
 Publication Date:
 OSTI Identifier:
 35991
 Report Number(s):
 CONF9408161
TRN: 94:0097530259
 Resource Type:
 Conference
 Resource Relation:
 Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 1519 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
 Country of Publication:
 United States
 Language:
 English
 Subject:
 22 NUCLEAR REACTOR TECHNOLOGY; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; COMPUTERIZED CONTROL SYSTEMS; OPTIMIZATION; MATRICES; NUMERICAL SOLUTION; NEWTON METHOD; ALGORITHMS; CONVERGENCE; ACCURACY
Citation Formats
Faco, J.L.D. On largescale nonlinear programming techniques for solving optimal control problems. United States: N. p., 1994.
Web.
Faco, J.L.D. On largescale nonlinear programming techniques for solving optimal control problems. United States.
Faco, J.L.D. 1994.
"On largescale nonlinear programming techniques for solving optimal control problems". United States.
doi:.
@article{osti_35991,
title = {On largescale nonlinear programming techniques for solving optimal control problems},
author = {Faco, J.L.D.},
abstractNote = {The formulation of decision problems by Optimal Control Theory allows the consideration of their dynamic structure and parameters estimation. This paper deals with techniques for choosing directions in the iterative solution of discretetime optimal control problems. A unified formulation incorporates nonlinear performance criteria and dynamic equations, time delays, bounded state and control variables, free planning horizon and variable initial state vector. In general they are characterized by a large number of variables, mostly when arising from discretization of continuoustime optimal control or calculus of variations problems. In a GRG context the staircase structure of the jacobian matrix of the dynamic equations is exploited in the choice of basic and super basic variables and when changes of basis occur along the process. The search directions of the bound constrained nonlinear programming problem in the reduced space of the super basic variables are computed by largescale NLP techniques. A modified PolakRibiere conjugate gradient method and a limited storage quasiNewton BFGS method are analyzed and modifications to deal with the bounds on the variables are suggested based on projected gradient devices with specific linesearches. Some practical models are presented for electric generation planning and fishery management, and the application of the code GRECO  Gradient REduit pour la Commande Optimale  is discussed.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 1994,
month =
}

Algorithmic enhancements and experience with a large scale SQP code for general nonlinear programming problems
We have developed a large scale sequential quadratic programming (SQP) code based on an interiorpoint method for solving general (convex or nonconvex) quadratic programs (QP). We often halt this QP solver prematurely by employing a trustregion strategy. This procedure typically reduces the overall cost of the code. In this talk we briefly review the algorithm and some of its theoretical justification and then discuss recent enhancements including automatic procedures for both increasing and decreasing the parameter in the merit function, a regularization procedure for dealing with linearly dependent active constraint gradients, and a method for modifying the linearized equality constraints.more »