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Numerical experiments with the Lancelot package (Release \(A\)) for large-scale nonlinear optimization. (English) Zbl 0848.90109
Summary: We describe the algorithmic options of Release A of Lancelot, a Fortran package for large-scale nonlinear optimization. We then present the results of intensive numerical tests and discuss the relative merits of the options. The experiments described involve both academic and applied problems. Finally, we propose conclusions, both specific to Lancelot and of more general scope.

MSC:
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
90C06 Large-scale problems in mathematical programming
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[1] D.P. Ahlfeld, R.S. Dembo, J.M. Mulvey and S.A. Zenios, ”Nonlinear programming on generalized networks,”ACM Transactions on Mathematical Software 13 (1987) 350–367.
[2] B.M. Averick, R.G. Carter and J.J., Moré, ”The Minpack-2 test problem collection (preliminary version),” Technical Report ANL/MCS-TM-150, Argonne National Laboratory (Argonne, IL, 1991).
[3] B.M. Averick and J.J. Moré, ”The Minpack-2 test problem collection,” Technical Report ANL/MCS-TM-157, Argonne National Laboratory (Argonne, IL, 1991).
[4] I. Bongartz, A.R. Conn, N. Gould and Ph.L. Toin. ”CUTE: Constrained and Unconstrained Testing Environment,”ACM Transactions on Mathematical Software 21 (1995) 121–160. · Zbl 0886.65058
[5] A.G. Buckley, ”Test functions for unconstrained minimization”, Technical Report CS-3, Computing Science Division, Dalhousie University (Dalhousie, Canada, 1989).
[6] J.V. Burke and J.J. Moré, ”On the identification of active constraints,”SIAM Journal on Numerical Analysis 25 (1988) 1197–1211. · Zbl 0662.65052
[7] J.V. Burke, J.J. Moré and G. Toraldo, ”Convergence properties of trust region methods for linear and convex constraints,”Mathematical Programming 47 (1990) 305–336. · Zbl 0711.90060
[8] P.H. Calamai and J.J. Moré, ”Projected gradient methods for linearly constrained problems,”Mathematical Programming 39 (1987) 93–116. · Zbl 0634.90064
[9] A.R. Conn, N. Gould, M. Lescrenier and Ph.L. Toint, ”Performance of a multifrontal scheme for partially separable optimization,” inAdvances in Optimization and Numerical Analysis, Proceedings of the Sixth Workshop on Optimization and Numerical Analysis, Oaxaca, Mexico (Kluwer, Dordrecht, Netherlands, 1994) pp. 79–96. · Zbl 0809.90117
[10] A.R. Conn, N. Gould and Ph.L. Toint, ”Global convergence of a class of trust region algorithms for optimization with simple bounds”.SIAM Journal on Numerical Analysis 25 (1988) 433–460 [See also same journal 26 (1989) 764–767. · Zbl 0643.65031
[11] A.R. Conn, N. Gould and Ph.L. Toint, ”Testing a class of methods for solving minimization problems with simple bounds on the variables,”Mathematics of Computation 50 (1988) 399–430. · Zbl 0645.65033
[12] A.R. Conn, N. Gould and Ph.L., Toint, ”An introduction to the structure of large scale nonlinear optimization problems and the LANCELOT project,” in: R. Glowinski and A. Lichnewsky, eds.,Computing Methods in Applied Sciences and Engineering (SIAM, Philadelphia, PA, 1990) pp. 42–51.
[13] A.R. Conn, N. Gould and Ph.L. Toint, ”A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds,”SIAM Journal on Numerical Analysis 28 (1991) 545–572. · Zbl 0724.65067
[14] A.R. Conn, N. Gould and Ph.L. Toint, ”A globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds,”Mathematics of Computation, to appear. · Zbl 0854.90125
[15] A.R. Conn, N. Gould and Ph.L. Toint, LANCELOT:a Fortran Package for Large-Scale Nonlinear Optimization (Release A), Springer Series in Computational Mathematics, Vol. 17 (Springer, Berlin, 1992). · Zbl 0761.90087
[16] A.R. Conn, N. Gould and Ph.L. Toint, ”On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear equality constrainst and simple bounds,” in: D.F. Griffiths and G.A. Walson, eds.,Proceedings of the 14th Biennal Numerical Analysis Conference Dundee 1991 (Longmans, London, 1992) pp. 49–68. · Zbl 0809.65066
[17] A.R. Conn, N. Gould and Ph.L. Toint, ”Convergence properties of minimization algorithms for convex constraints using a structured trust region”SIAM Journal on Optimization, to appear. · Zbl 0868.90106
[18] A.R. Conn, N. Gould and Ph.L. Toint, ”Intensive numerical tests with LANCELOT (Release A): the complete results,” Technical Report 92/15, Department of Mathematics, FUNDP (Namur, Belgium, 1992).
[19] A.R. Conn, N. Gould and Ph.L. Toint, ”A note on exploiting structure when using slack variables,”Mathematical Programming 67 (1994) 89–97. · Zbl 0827.90126
[20] A.R. Curtis and J.K. Reid, ”On the automatic scaling of matrices for Gaussian eliminantion,”Journal of the Institute of Mathematics and its Applications 10 (1972) 118–124. · Zbl 0249.65026
[21] R.S. Dembo, ”A primal truncated-newton algorithm with application to large-scale nonlinear network optimization,” Technical Report 72, Yale School of Management (Yale University, New Haven, CT, 1984). · Zbl 0635.90072
[22] R.S. Dembo,” The performance of NLPNET, a large scale nonlinear network optimizer”,Mathematical Programming 26 (1986) 245–249. · Zbl 0592.90089
[23] J.E. Dennis and R.B. Schnabel,Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, NJ, 1983). · Zbl 0579.65058
[24] L.C.W. Dixon, ”On automatic differentiation and continuous optimization,” in: E. Spedicato, ed.,Algorithms for Continuous Optimization: the State of the Art (Kluwer, Dordrecht, 1994) pp. 501–513. · Zbl 0829.90111
[25] I.S. Duff, A.M. Erismann and J.K. Reid,Direct Methods for Sparse Matrices (Clarendon Press, Oxford, 1986). · Zbl 0604.65011
[26] I.S. Duff and J.K. Reid, ”MA27: A set of Fortran subroutines for solving sprrse symmetric sets of linear equations,” Report R-10533, AERE Harwell Laboratory (Harwell, UK, 1982).
[27] I.S. Duff and J.K. Reid, ”The multifrontal solution of indefinite sparase symmetric linear equations,”ACM Transactions on Mathematical Software 9 (1983) 302–325. · Zbl 0515.65022
[28] R. Fletcher,Practical Methods of Optimization (Wiley, Chichester, 2nd ed., 1987). · Zbl 0905.65002
[29] A. George and J.W.-H., Liu,Computer Solution of Large Sparse Positive Definite Systems (Prentice-Hall, Englewood Cliffs, NJ, 1981).
[30] P.E. Gill, W. Murray, D.B. Ponceléon and M.A. Saunders, ”Preconditioners for indefinite systems arising in optimization,”SIAM Journal on Matrix Analysis and Applications 13 (1992) 292–311. · Zbl 0749.65037
[31] P.E. Gill, W. Murray and M.H. Wright,Practical Optimization (Academic Press, London, 1981).
[32] G.H. Golub and C.F. Van Loan,Matrix Computations (Johns Hopkins University Press, Baltimore, MD, 2nd ed., 1989). · Zbl 0733.65016
[33] A. Griewank, ”Computational differentiation and optimization,” in: J.R. Birge and K.G. Murty, eds.,Mathematical Programming: State of the Art 1994 (The University of Michigan, Ann Arbor, MI, 1994) pp. 102–131.
[34] A. Grieqank and Ph.L. Toint, ”On the unconstrained optimization of partially separable functions,” in: M.J.D. Powell, ed.,Nonlinear Optimization 1981 (Academic Press, London, 1982) pp. 301–312.
[35] M. Gulliksson, ”Algorithms for nonlinear least squares with applications to orthogonal regression,” Ph.D. Thesis, Institute of Information Processing, University of Umeå (1990).
[36] W. Hock and K. Schittkowski,Test Examples for Nonlinear Programming Codes, Lectures Notes in Economics and Mathematical Systems Vol. 187 (Springer, Berlin, 1981). · Zbl 0452.90038
[37] M.M. Kostreva, ”Elasto-hydrodynamic lubrification: a non-linear complementarity problem,”Interational Journal for Numerical Methods in Fluids 4 (1984) 377–397. · Zbl 0551.76007
[38] M. Lescrenier, ”Convergence of trust region algorithms for optimization with bounds when strict complementarity does not hol,”SIAM Journal on Numerical Analysis 28 (1991) 476–495. · Zbl 0726.65068
[39] A. Lewis, private communication (1990).
[40] J.J. Moré, ”Trust regions and projected gradients,” in: M. Iri and K. Yajima, eds.,System Modelling and Optimization, Lecture Notes in Control and Information Sciences Vol. 113, (Springer, Berlin, 1988) pp. 1–13. · Zbl 0655.90069
[41] J.J. Moré, ”A collection of nonlinear model problems”, Technical Report ANL/MCS-P60-0289, Argonne National Laboratory (Argonne, IL, 1989).
[42] J.J. Moré, B.S. Garbow and K.E. Hillstrom, ”Testing unconstrained optimization software,”ACM Transactions on Mathematical Software 7 (1981) 17–41. · Zbl 0454.65049
[43] J.J. Moré and G. Toraldo, ”On the solution of large scale quadratic programming problems with bound constraints,”SIAM Journal on Optimization 1 (1991) 93–113. · Zbl 0752.90053
[44] N. Munksgaard, ”Solving sparse symmetric systems of linear equations by preconditioned conjugate gradients,”ACM Transactions on Mathematical Software 6 (1980) 206–219. · Zbl 0438.65035
[45] B.A. Murtagh and M.A. Saunders, ”MINOS 5.1 USER’S GUIDE,” Technical Report SOL83-20R, Department of Operations Research, Stanford University (Stanford, CA, 1987).
[46] A. Sartenaer, ”A class of trust region methods for nonlinear network optimization problems,”SIAM Journal of Optimization, 5 (1995) 379–407. · Zbl 0834.90134
[47] K. Schittkowski, ”More Test Examples for Nonlinear Programming Codes,” Lecture Notes in Economics and Mathematical Systems Vol. 282 (Springer, Berlin, 1987) · Zbl 0658.90060
[48] T. Schlick, ”Modified Cholesky factorizations for sparse preconditioners,”SIAM Journal on Scientific and Statistical Computing 14 (1993) 424–445. · Zbl 0771.65031
[49] R.B. Schnabel and E. Eskow, ”A new modified Cholesky factorization,”SIAM Journal on Scientific and Statistical Computing 11 (1991) 1136–1158. · Zbl 0716.65023
[50] Ph.L. Toint, ”Test problems for partially separable optimization and results for the routine PSPMIN,” Technical Report 83/4, Department of Mathematics, FUNDP (Namur, Belgium, 1983).
[51] Ph.L. Toint, ”Global convergence of a class of trust region methods for nonconvex minimization in Hilbert space,”IMA Journal of Numerical Analysis 8 (1988) 231–252. · Zbl 0698.65043
[52] Ph.L. Toint and D. Tuyttens, ”On large scale nonlinear network optimization,”Mathematical Programming 48 (1990) 125–159. · Zbl 0693.90092
[53] Ph.L. Toint and D. Tuyttens, ”LSNNO: a Fortran subroutine for solving large scale nonlinear network optimization problems,”ACM Transactions on Mathematical Software 18 (1992) 308–328. · Zbl 0892.65033
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