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How much do approximate derivatives hurt filter methods? (English) Zbl 1175.65074
Summary: We examine the influence of approximate first and/or second derivatives on the filter-trust-region algorithm designed for solving unconstrained nonlinear optimization problems and proposed by N. I. M. Gould, C. Sainvitu and P. L. Toint [SIAM J. Optim. 16, No. 2, 341–357 (2005; Zbl 1122.90074)]]. Numerical experiments carried out on small-scaled unconstrained problems from the CUTEr collection describe the effect of the use of approximate derivatives on the robustness and the efficiency of the filter-trust-region method.

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C51 Interior-point methods
Full Text: DOI EuDML
[1] R.H. Byrd, P. Lu, J. Nocedal and C. Zhu, A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput.16 (1995) 1190-1208. Zbl0836.65080 · Zbl 0836.65080 · doi:10.1137/0916069
[2] A.R. Conn, N.I.M. Gould and P.L. Toint, Convergence of quasi-Newton matrices generated by the Symmetric Rank One update. Math. Program.50 (1991) 177-196. · Zbl 0737.90062 · doi:10.1007/BF01594934
[3] A.R. Conn, N.I.M. Gould and P.L. Toint, Trust-Region Methods. MPS-SIAM Series on Optimization 1, SIAM, Philadelphia, USA (2000). · Zbl 0958.65071
[4] A.R. Conn, K. Scheinberg and P.L. Toint, Recent progress in unconstrained nonlinear optimization without derivatives. Math. Program. Ser. B79 (1997) 397-414. · Zbl 0887.90154 · doi:10.1007/BF02614326
[5] E.D. Dolan and J.J. MorĂ©, Benchmarking optimization software with performance profiles. Math. Program.91 (2002) 201-213. Zbl1049.90004 · Zbl 1049.90004 · doi:10.1007/s101070100263
[6] R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function. Math. Program.91 (2002) 239-269. · Zbl 1049.90088 · doi:10.1007/s101070100244
[7] N.I.M. Gould, S. Leyffer and P.L. Toint, A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares. SIAM J. Optim.15 (2005) 17-38. Zbl1075.65075 · Zbl 1075.65075 · doi:10.1137/S1052623403422637
[8] N.I.M. Gould, S. Lucidi, M. Roma and P.L. Toint, Solving the trust-region subproblem using the Lanczos method. SIAM J. Optim.9 (1999) 504-525. Zbl1047.90510 · Zbl 1047.90510 · doi:10.1137/S1052623497322735
[9] N.I.M. Gould, D. Orban, A. Sartenaer and P.L. Toint, Sensitivity of trust-region algorithms on their parameters. 4OR, Quarterly Journal of Operations Research 3 (2005) 227-241. Zbl1086.65060 · Zbl 1086.65060 · doi:10.1007/s10288-005-0065-y
[10] N.I.M. Gould, D. Orban and P.L. Toint, CUTEr, a constrained and unconstrained testing environment, revisited ACM Trans. Math. Software29 (2003) 373-394. Zbl1068.90526 · Zbl 1068.90526 · doi:10.1145/962437.962439
[11] N.I.M. Gould, D. Orban and P.L. Toint, GALAHAD - a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. ACM Trans. Math. Software29 (2003) 353-372. Zbl1068.90525 · Zbl 1068.90525 · doi:10.1145/962437.962438
[12] N.I.M. Gould, C. Sainvitu and P.L. Toint, A Filter-Trust-Region Method for Unconstrained Optimization. SIAM J. Optim.16 (2005) 341-357. · Zbl 1122.90074 · doi:10.1137/040603851
[13] N.I.M. Gould and P.L. Toint, FILTRANE, a Fortran 95 Filter-Trust-Region Package for Solving Systems of Nonlinear Equalities, Nonlinear Inequalities and Nonlinear Least-Squares Problems. Technical report 03/15, Rutherford Appleton Laboratory, Chilton, Oxfordshire, UK (2003).
[14] D.C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization. Math. Program. Ser. B45 (1989) 503-528. Zbl0696.90048 · Zbl 0696.90048 · doi:10.1007/BF01589116
[15] D.F. Shanno and K.H. Phua, Matrix conditionning and nonlinear optimization. Math. Program.14 (1978) 149-160. · Zbl 0371.90109 · doi:10.1007/BF01588962
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