Автор |
Conforti, D. |
Автор |
Grandinetti, L. |
Автор |
Musmanno, R. |
Дата выпуска |
1994 |
dc.description |
A new iterative algorithm for solving unconstrained optimization problems is introduced. It is based on the construction, at each iteration, of a curvilinear path to be searched for a local solution. Since the curvilinear path is denned by using a tensor of third order partial derivatives of the objective function, efficient and reliable implementations can benefit of powerful computational tools like parallel computing and automatic differentiation. Computational experiments were carried out with the aim to compare the proposed algorithm with well known Newton type algorithms. It turns out that the proposed algorithm is very efficient especially in the case of badly scaled and ill-conditioned problems. |
Формат |
application.pdf |
Издатель |
Gordon and Breach Science Publishers |
Копирайт |
Copyright Taylor and Francis Group, LLC |
Тема |
unconstrained optimization |
Тема |
nonlinear optimization |
Тема |
curvilinear path |
Тема |
tensor algorithm |
Тема |
parallel computing |
Тема |
automatic differentiation |
Название |
A parallel tensor algorithm for nonlinear optimization |
Тип |
other |
DOI |
10.1080/10556789408805560 |
Electronic ISSN |
1029-4937 |
Print ISSN |
1055-6788 |
Журнал |
Optimization Methods and Software |
Том |
3 |
Первая страница |
125 |
Последняя страница |
142 |
Аффилиация |
Conforti, D.; DEIS — Dipartimento di Elettronica, Infomatica e Sistemistica, Universitá della Calabrin |
Аффилиация |
Grandinetti, L.; DEIS — Dipartimento di Elettronica, Infomatica e Sistemistica, Universitá della Calabrin |
Аффилиация |
Musmanno, R.; DEIS — Dipartimento di Elettronica, Infomatica e Sistemistica, Universitá della Calabrin |
Выпуск |
1-3 |
Библиографическая ссылка |
Fletcher, R. 1987. Practical Methods for Optimization, John Wiley and Son. |
Библиографическая ссылка |
Gill, P.E., Murray, W. and Wright, M.H. 1987. Practical Optimization, Academic Press. |
Библиографическая ссылка |
Bertsekas, D.P. and Tsitsiklis, J.N. 1989. Parallel and Distributed Computation-Numerical Methods, Prentice-Hall. |
Библиографическая ссылка |
Griewank, A. 1989. “On automatic differentiation”. In Mathematical Programming Recent Developments and Applications, Edited by: Iriad, M. and Tanabe, K. 83–108. Dordrecht: Kluwer Academic Publishers. |
Библиографическая ссылка |
Grandinetti, L. Nonlinear Optimization by a Curvilinear Path Strategy. Proceedings of the 11th IFIP Conference. Edited by: Thoft-Cristiansen, P. Lecture Notes in Control and Information Sciences |
Библиографическая ссылка |
Goldfarb, D. 1980. Curvilinear path steplength algorithms for minimization which use directions of negative curvature. Mathematical Programming, 18: 31–40. |
Библиографическая ссылка |
Rail, L.B. 1981. “Automatic Differentation Techniques and Applications”. Vol. 120, Berlin: Springer Verlag. Lecture Notes in Computer Science |
Библиографическая ссылка |
Iri, M. and Kubota, K. 1987. Methods of Fast Automatic Differentiation and Applications Department of Mathematical Engineering and Information Physics, Faculty of Engineering, University of Tokio. Research Memorandum RMI 87-02 |
Библиографическая ссылка |
Bishof, C.H. 1991. “Parallel Automatic Differentiation”. In Automatic Differentiation ofAlgorithms: Theoty, Implementations and Application Edited by: Griewank, A. and Corliss, G.F. 100–113. Proceedings of the SIAM Workshop on the Automatic Differentiation Algorithms |
Библиографическая ссылка |
Fischer, H. 1990. Automatic Differentiation Parallel Computation of Function, Gradient and Hessian Matrix. Parallel Computing, 13: 101–110. |
Библиографическая ссылка |
Ortega, J.M. 1988. Introduction to Parallel and Vector Solution of Linear Systems, Plenum Press. |
Библиографическая ссылка |
Harwell Subroutine Library Specification. 1990. “Advanced Computing Department”. 765–767. Oxfordshire, England: Harwell Laboratory. |
Библиографическая ссылка |
Brown, A.A. and Bartholomew-Biggs, M.C. 1987. “Some Effective Methods for Unconstrained Optimization Based on the Solution of Systems of Ordinary Differential Equations”. Hatfield, England: The Hatfield Polytechnic. Technical Report No. 178, Numerical Optimization Centre |
Библиографическая ссылка |
Leon, A. 1966. “A Comparison among Eight Known Optimizing Procedures ”. In Recent Advances in Optimization Techniques, Edited by: Lavi, A. and Vogl, T. 28–46. New York: John Wiley and Sons. |
Библиографическая ссылка |
Moré, J.J., Garbow, B.S. and Hillstrom, K.E. 1981. Testing Unconstrained Optimization Software. ACM Transactions on Mathematical Software, 7: 17–41. |
Библиографическая ссылка |
1990. “Harwell Subroutine Library Specification, Advanced Computing Department”. 732–735. Oxfordshire, England: Harwell Laboratory. |
Библиографическая ссылка |
Gay, D.M. 1983. Algorithm 611 Subroutine for unconstrained minimization using a model trust region approach. ACM Transactions on Mathematical Software, 9: 503–524. |
Библиографическая ссылка |
Nash, S.G. and Sofer, A. 1989. Block Truncated-Newton methods for parallel optimization. Mathematical Programming, 45: 529–546. |
Библиографическая ссылка |
Dixon, L.C.W. and Price, R.C. 1988. Numerical Experience with the Truncated Newton Method for Unconstrained Optimization. JOTA, 56(2) |
Библиографическая ссылка |
Grippo, L., Lampariello, F. and Lucidi, S. 1989. A Truncated Newton Method with Nonmonotone Line Search for Unconstrained Optimization. JOTA, 60(3): 401–419. |
Библиографическая ссылка |
Grippo, L., Lampariello, F. and Lucidi, S. 1990. A Quasi-Discrete Newton Algorithm with a Nonmonotone Stabilization Technique. JOTA, 64(3): 495–510. |
Библиографическая ссылка |
Dennis, J.E. and Schnabel, R.B. 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall. |
Библиографическая ссылка |
Bartholomew-Biggs, M.C. 1983. Minimization algorithms making use of non quadratic properties of the. |
Библиографическая ссылка |
1990. Hanvell Subroutine Library Specification, 727–731. Oxfordshire, , England: Advanced Computing Department, Hanvell Laboratory. |
Библиографическая ссылка |
Zang, I. 1978. A New Arc Algorithm for Unconstrained Optimization. Mathematical Programming, 15: 36–52. |