Nonlinear constrained optimizer and parallel processing for golden block line search

• Autorzy: Nguyen D. T. , Tang W. H. , Tung Y. K. , Runesha H. B.
• Konferencja: International Conference on Numerical Mathematics and Computational Mechanics : NMCM'98 (8 th ; August 1998 ; Miskolc ; Hungary)
• Języki publikacji: EN

Abstrakty

EN

Generalized exponential penalty functions are constructed for the multiplier methods in solving nonlinear programming problems. The non-smooth extreme constraint Gext is replaced by a single smooth constraint Gs by using the generalized exponential function (base a>1). The well-known K.S. function is found to be a special case of our proposed formulation. Parallel processing for Golden block line search algorithm is then summarized, which can also be integrated into our formulation. Both small and large-scale nonlinear programming problems (up to 2000 variables and 2000 nonlinear constraints) have been solved to validate the proposed algorithms.

Słowa kluczowe

EN

nonlinear programming; parallel processing

PL

programowanie nieliniowe; przetwarzanie równoległe

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 1999
• Tom: Vol. 6, No. 3-4
• Strony: 469--477
• Opis fizyczny: Bibliogr. 15 poz., tab.

Twórcy

autor

Nguyen D. T.

• Multidisciplinary Parallel-Vector Computation Center, Kaufman 135, Old Dominion University, Norfolk, VA 23529, USA

autor

Tang W. H.

• Department of Civil and Structural Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong

autor

Tung Y. K.

• Department of Civil and Structural Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong

autor

Runesha H. B.

• Multidisciplinary Parallel-Vector Computation Center, Kaufman 135, Old Dominion University, Norfolk, VA 23529, USA

Bibliografia

• [1] G. Kreisselmeier, R. Steinhauser. Systematic control design by optimizing a vector performance index. Proc. IFAC Symp. on Computer Aided Design of Control System. Zurich, Switzerland, 1979.
• [2] G.P. McCormick. Nonlinear Programming, Theory, Algorithm, and Applications. John Wiley and Sons, New York, 1983.
• [3] M.J.D. Powell. A method for nonlinear constraints in minimization problems. In: R. Fletcher, ed., Optimization, 283-298. Academic, London, 1969.
• [4] M.R. Hestenes. Multiplier and gradient methods. J. Optim. Theor. Appl., 4(5): 303-320, 1969.
• [5] A.B. Templeman, X.S. Li. A maximum entropy approach to constrained non-linear programming. Eng. Optimization, 12: 191-205, 1987.
• [6] X.S. Li. An aggregate function method for nonlinear programming. Science in China, (series A), 34: 1467-1473, 1991.
• [7] P. Hajela. Further developments in the controlled growth approach for optimal structural synthesis. ASME Paper 82-DET-62, 1982.
• [8] P. Hajela. A look at two underutilized methods for optimum structural design. Eng. Optimization, 11: 21-30, 1987.
• [9] J. Sobieszczanski-Sobieski, B.B. James, A.R. Dovi. Structural optimization by multilevel decomposition. AJAA J., 23: 1775-1782, 1985.
• [10] J. Sobieszczanski-Sobieski, A.R. Dovi, G.A. Wrenn. A new algorithm for general multiobjective optimization. Proc. AIAA/ASME/ASCE/AHS 29th Structural Dynamics and Materials Conference, Williamsburg, Virginia, Paper 88-2434, 1988.
• [11] J.S. Arora, A.I. Chahande, J.K. Paeng. Multiplier methods for engineering optimization. Int. J. Num. Meths. Eng., 32: 1485-1525, 1991.
• [12] W. Hock, K. Schittkowski, Test Examples for Nonlinear Programming Codes Springer-Verlag, Berlin—Heidelberg, 1981.
• [13] J.S. Arora. Introduction to Optimum Design, McGraw-Hill Inc., 1989.
• [14] R.T. Haftka, Z. Gurdal, M.P. Kamat. Elements of Structural Optimization, 2nd Edition. Kluwer Academic, 1990.
• [15] T.K. Agarwal, O.O. Storaasli, D.T. Nguyen. A parallel-vector algorithm for rapid structural analysis on high-performance computers. Proc. of AIAA/ASME/ASCE/AHS 31st SDM Conference, Long Beach, CA April 2-4, 1990, AIAA paper No. 90-1149, 1990.