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A truncated SQP algorithm for solving nonconvex equality constrained optimization problems

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High Performance Algorithms and Software for Nonlinear Optimization

Part of the book series: Applied Optimization ((APOP,volume 82))

Abstract

An algorithm for solving equality constrained optimization problems is proposed. It can deal with nonconvex functions and uses the truncated conjugate gradient algorithm for detecting nonconvexity. The algorithm ensures convergence from remote starting point by using line-search. Numerical experiments are reported, comparing the approach with the one implemented in the trust region codes ETR and Knitro.

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References

  1. J.T. Betts (2001).Practical Methods for Optimal Control Using Nonlinear Programming. SIAM.

    MATH  Google Scholar 

  2. P.T. Boggs, J.W. Tolle (1995). Sequential quadratic programming. In Acta Numerica 1995, pages 1–51. Cambridge University Press.

    Google Scholar 

  3. I. Bongartz, A.R.Conn, N.I.M. Gould, Ph.L. Toint (1995). CUTE: Constrained and unconstrained testing environment. ACM Transactions on Mathematical Software, 21, 123–160.

    Article  MATH  Google Scholar 

  4. J.F. Bonnans, J.Ch. Gilbert, C. Lemaréchal, C. Sagastizábal (2002). Numerical Optimization - Theoretical and Practical Aspects. Springer Verlag, Berlin. (to appear).

    Google Scholar 

  5. R.H. Byrd (1987, May). Robust trust region methods for constrained optimization. Third SIAM Conference on Optimization, Houston, TX.

    Google Scholar 

  6. R.H. Byrd, J.Ch. Gilbert, J. Nocedal (2000). A trust region method based on interior point techniques for nonlinear programming. Mathematical Programming, 89, 149–185.

    Article  MathSciNet  MATH  Google Scholar 

  7. R.H. Byrd, M.E. Gilbert, J. Nocedal (1999). An interior point algorithm for large scale nonlinear programming. SIAM Journal on Optimization, 9, 877–900.

    Article  MathSciNet  MATH  Google Scholar 

  8. L. Chauvier (2000). Commande Optimale d’Engins Sous-Marins avec Contraintes. Thèse de doctorat, Université Paris I (Panthéon-Sorbonne).

    Google Scholar 

  9. L. Chauvier, G. Damy, J.Ch. Gilbert, N. Pichon (1998). Optimal control of a deep-towed vehicle by optimization techniques. In Proceedings of the IEEE/OES Conference ”Oceans’98”, Nice, France, pages 1634–1639.

    Google Scholar 

  10. A.R. Conn, N. Gould, P.L. Toint (2000). Trust-Region Methods. MPS/SIAM Series on Optimization 1. SIAM and MPS.

    Google Scholar 

  11. R.S. Dembo, T. Steihaug (1983). Truncated-Newton algorithms for large-scale unconstrained optimization. Mathematical Programming, 26, 190–212.

    Article  MathSciNet  MATH  Google Scholar 

  12. E.D. Dolan, J.J. Moré (2002). Benchmarking optimization software with performance profiles. Mathematical Programming,91, 201–213.

    Article  MathSciNet  MATH  Google Scholar 

  13. R. Fletcher (1987). Practical Methods of Optimization (second edition). John Wiley & Sons, Chichester.

    MATH  Google Scholar 

  14. A. Fuduli, J.Ch. Gilbert (2002). OPINeL: a truncated Newton interior-point algorithm for nonlinear optimization. Technical report, INRIA, BP 105, 78153 Le Chesnay, France. (to appear).

    Google Scholar 

  15. J.Ch. Gilbert, X. Jonsson (1997). Méthodes à régions de confiance pour l’optimisation surfacique de verres ophtalmiques progressifs. Rapport de fin de contrat Essilor-Inria, référence 1–97-D-577–00–21105–012, INRIA, BP 105, 78153 Le Chesnay, France.

    Google Scholar 

  16. J.Ch. Gilbert, X. Jonsson (2002). BFGS preconditioning of a trust region algorithm for unconstrained optimization. Rapport de recherche, INRIA, BP 105, 78153 Le Chesnay, France. (to appear).

    Google Scholar 

  17. X. Jonsson (2002). Méthodes de Points Intérieurs et de Régions de Confiance en Optimisation Non Linéaire - Application à la Conception Optimale de Verres Ophtalmiques Progressifs. Thèse de doctorat, Université Paris VI.

    Google Scholar 

  18. M. Lalee, J. Nocedal, T. Plantenga (1998). On the implementation of an algorithm for large-scale equality constrained optimization. SIAM Journal on Optimization,8, 682–706.

    Article  MathSciNet  MATH  Google Scholar 

  19. N. Maratos (1978). Exact penalty function algorithms for finite dimensional and control optimization problems. PhD Thesis, Imperial College, London.

    Google Scholar 

  20. D.Q. Mayne, E. Polak (1982). A superlinearly convergent algorithm for constrained optimization problems. Mathematical Programming Study, 16, 45–61.

    Article  MathSciNet  MATH  Google Scholar 

  21. B. Mohammadi, O. Pironneau (2001). Applied Shape Optimization for Fluids. Oxford University Press.

    MATH  Google Scholar 

  22. J.L. Morales, J. Nocedal (2000). Automatic preconditioning by limited memory quasi-Newton updating. SIAM Journal on Optimization,10, 1079–1096.

    Article  MathSciNet  MATH  Google Scholar 

  23. S.G. Nash (1984). Truncated-Newton methods for large-scale function minimization. In H.E. Rauch (editor), Application of Nonlinear Programming to Optimization and Control, pages 91–100. Pergamon Press, Oxford.

    Google Scholar 

  24. J. Nocedal, R.A. Waltz (2001). KNITRO 1.00 – User’s manual. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, Il 60208, USA.

    Google Scholar 

  25. J. Nocedal, S.J. Wright (1999). Numerical Optimization. Springer Series in Operations Research. Springer, New York.

    Google Scholar 

  26. E.O. Omojokun (1991). Trust region algorithms for optimization with nonlinear equality and inequality constraints. PhD Thesis, Department of Computer Science, University of Colorado, Boulder, Colorado 80309.

    Google Scholar 

  27. E. Polak (1997). Optimization - Algorithms and Consistent Approximations. Applied Mathematical Sciences 124. Springer, Paris.

    MATH  Google Scholar 

  28. T. Steihaug (1983). The conjugate gradient method and trust regions in large scale optimization. SIAM Journal on Numerical Analysis, 20, 626–637.

    Article  MathSciNet  MATH  Google Scholar 

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© 2003 Kluwer Academic Publishers B.V.

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Chauvier, L., Fuduli, A., Gilbert, C.J. (2003). A truncated SQP algorithm for solving nonconvex equality constrained optimization problems. In: Di Pillo, G., Murli, A. (eds) High Performance Algorithms and Software for Nonlinear Optimization. Applied Optimization, vol 82. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0241-4_7

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  • DOI: https://doi.org/10.1007/978-1-4613-0241-4_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7956-0

  • Online ISBN: 978-1-4613-0241-4

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