A quasi-Newton interior point algorithm applied to constrained optimum design in computational fluid dynamics
Keywords:
interior points, feasible sets, quasi-Newton, dejlexion, line search, adjoint state, CFDAbstract
This paper introduces and describes a second order interior point method well adapted to. constrained shape optimal design in engineering. The· theoritical background is presented and detailed implementation procedures are given in the case of nonlinear inequality constraints. The algorithm is then applied to two significative shape optimum problems in Computational Fluid dynamics.
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References
AUATT, S. S., Nonlinear Programming Algorithms for Elastic Contact Problems,
(in Portuguese), COPPE, Federal University of Rio de Janeiro, Brazil, MS
Thesis, 1993.
BARON, F. J. AND PIRONNEAU, 0., Multidisciplinary Optimal Design of a
Wing Profile, Proceedings of STRUCTURAL OPTIMIZATION 93, Rio de
Janeiro, Edited by J. Herskovits, 8/1993.
BARON, F. J. Constrained Shape Optimization of Coupled Problems with Electromagnetic
Waves and Fluid Mechanics, (in Spanish), University of Malaga,
Spain, PhD Thesis, 1994.
BARON, F. J., DUFF A, G., CARRERE, F. AND LE TALLEC, P., Optimisation de
forrne en aerodynamique, (in French), CHOCS, Revue scientifique et technique
de la Direction des Applications Militaires du CEA, France, 1994.
GILBERT J.-C., LEVEY G. AND MASSE J., La differentiation automatique de
fonctions representees par des programmes, INRIA Research Report RR1557,
HERSKOVITS, J ., A Two-Stage Feasible Directions Algorithm for Non-Linear
Constrained Optimization, Research Report No. 103, INRIA, BP 105,78153 Le
Chesnay CEDEX, France, 1982.
HERSKOVITS, J ., A Two-Stage Feasible Directions Algorithm Including Variable
Metric Techniques for Nonlinear Optimization, Research Report nO 118,
INRIA, BP 105, 78153 Le Chesnay CEDEX, France, 1982.
pour
HERSKOVITS, J., A Two-Stage Feasible Directions Algorithm for Nonlinear
Constrained Optimization , Mathematical Programming, Vol. 36, pp. 19-38,
HERSKOVITS, J. AND COELHO, C.A.B. An Interior Point Algorithm for Structural
Optimization Problems , in Computer Aided Optimum Design of Structures:
Recent Advances, edited by C.A. Brevia and S.Hemandez, Computational
Mechanics Publications, Springer-Verlag, June 1989.
HERSKOVITS, J .,An Interior Point Technique for Nonlinear Optimization, Research
Report No. 1808, INRIA, BP 105, 78153 Le Chesnay CEDEX, France,
HERSKOVITS, J .,An Interior Point Technique for Nonlinear Optimization, Research
Report No. 1808, INRIA, BP 105, 78153 Le Chesnay CEDEX, France,
HERSKOVITS, J ., A View on Nonlinear Optimization, Advances in Structural
Optimization, Edited by J. Herskovits, Kluwer Academic Publishers, Dordrecht,
pp 71-117, 1995.
HIRIART-URRUTY, J. B. AND LEMARECHAL, C. Convex analysis and Minimization
Algorithms, Springer- Verlag, Berlin, Heildelberg, 1993.
MOHAMMADI B., Fluid dynamics computation with NSC2KE: an user-guide:
release 1.0., INRIA Technical ReportRT0164, 1994.
POWELL M. J. D., Variable Metric Methods for Constrained Optimization, in
Mathematical Programming - The State of the Art, Edited by A. Bachem, M.
Grotschet and B. Korte, Springer-Verlag, Berlin, 1983.
SANTOS, G., Feasible Directions Interior Point Algorithms for Engineering Optimization
, (in Portuguese), DSc. Dissertation, COPPE - Federal University of
Rio de Janeiro, Mechanical Engineering Program, Caixa Posta168503, 21945-
, Rio de Janeiro, Brazil, 1996.
TITS, A.L., ZHOU, J.L. A Simple, Quadratically Convergent Interior Point Algorithm
for Linear Programming and Convex Quadratic Programming, Large
Scale Optimization: State of the Art, W.W. Hager, D.W. Hearn and P.M. Pardalos
Eds., Kluwer Academic Publishers B.V., 1993.
VAUTIER, 1., SALAUN, M. AND HERSKOVITS, J., Application of an Interior
Point Algorithm to the Modeling of Unilateral Contact Between Spot-Welded
Shells, Proceedings of STRUCTURAL OPTIMIZATION 93, Rio de Janeiro,
Edited by J. Herskovits, 8!1993.
ZOUAIN, N.A., HERSKOVITS J., BORGES, L.A. AND FEIJOO, R. An Iterative
Algorithm for Limit Analysis with Nonlinear Yield Functions, International
Journal on Solids and Structures, Vol30,No lO,pp 1397-1417, Gt. Britain, 1993.