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Erschienen in: Journal of Applied Mathematics and Computing 1-2/2015

01.06.2015 | Original Research

An efficient implementation of a trust region method for box constrained optimization

verfasst von: Hamid Esmaeili, Morteza Kimiaei

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2015

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Abstract

The present research deals with a trust-region-based procedure to solve box constrained optimization problems. Our procedure takes the advantage of the compact limited memory BFGS update formula together with an adaptive radius strategy. This adaptive technique leads to decreasing the number of solved subproblems and the total number of iterations, while utilizing the structure of limited memory quasi-Newton formula helps us to handle large-scale problems. Using classical assumptions, we prove that our method is a global convergence to first-order stationary points. Preliminary numerical experiments indicate that our new approach is considerably promising to solve box constrained optimization problems, especially for large-scale ones.

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Literatur
1.
Zurück zum Zitat Ahookhosh, M., Amini, K.: A nonmonotone trust region method with adaptive radius for unconstrained optimization problems. Comput. Math. Appl. 60, 411–422 (2010)CrossRefMATHMathSciNet Ahookhosh, M., Amini, K.: A nonmonotone trust region method with adaptive radius for unconstrained optimization problems. Comput. Math. Appl. 60, 411–422 (2010)CrossRefMATHMathSciNet
2.
Zurück zum Zitat Birgin, E.G., Martínez, J.M., Raydan, M.: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10, 1196–1121 (2000)CrossRefMATHMathSciNet Birgin, E.G., Martínez, J.M., Raydan, M.: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10, 1196–1121 (2000)CrossRefMATHMathSciNet
3.
Zurück zum Zitat Birgin, E.G., Martínez, J.M., Raydan, M.: Algorithm 813: SPGsoftware for convex-constrained optimization. ACM Trans. Math. Softw. 27, 340–349 (2001)CrossRefMATH Birgin, E.G., Martínez, J.M., Raydan, M.: Algorithm 813: SPGsoftware for convex-constrained optimization. ACM Trans. Math. Softw. 27, 340–349 (2001)CrossRefMATH
5.
Zurück zum Zitat Burke, J.V., Xu, L.: An active set \(\ell _{\infty }\)-trust region algorithm for box constrained optimization. Department of Mathematics, University of Washington, Seattle, Technical Report preprint (2007) Burke, J.V., Xu, L.: An active set \(\ell _{\infty }\)-trust region algorithm for box constrained optimization. Department of Mathematics, University of Washington, Seattle, Technical Report preprint (2007)
6.
Zurück zum Zitat Byrd, R., Nocedal, J., Schnabel, R.: Representation of quasi-Newton matrices and their use in limited memory methods. Math. Progr. 63, 129–156 (1994)CrossRefMATHMathSciNet Byrd, R., Nocedal, J., Schnabel, R.: Representation of quasi-Newton matrices and their use in limited memory methods. Math. Progr. 63, 129–156 (1994)CrossRefMATHMathSciNet
7.
Zurück zum Zitat Byrd, R.H., Lu, P., Nocedal, J., Zhu, C.: A limited memory algorithm for bunded constrained optimization. SIAM J. Sci. Stat. Comput. 16, 1190–1208 (1995)CrossRefMATHMathSciNet Byrd, R.H., Lu, P., Nocedal, J., Zhu, C.: A limited memory algorithm for bunded constrained optimization. SIAM J. Sci. Stat. Comput. 16, 1190–1208 (1995)CrossRefMATHMathSciNet
8.
Zurück zum Zitat Conn, A.R., Gould, N.I.M., Toint, PhL: Testing a class of methods for solving minimization problems with simple bounded on the variables. Math. Comput. 50, 399–430 (1988)CrossRefMATHMathSciNet Conn, A.R., Gould, N.I.M., Toint, PhL: Testing a class of methods for solving minimization problems with simple bounded on the variables. Math. Comput. 50, 399–430 (1988)CrossRefMATHMathSciNet
9.
Zurück zum Zitat Conn, A.R., Gould, N.I.M., Toint, PhL: Trust-region methods. Society for Industrial and Applied Mathematics, SIAM, Philadelphia (2000)CrossRefMATH Conn, A.R., Gould, N.I.M., Toint, PhL: Trust-region methods. Society for Industrial and Applied Mathematics, SIAM, Philadelphia (2000)CrossRefMATH
10.
Zurück zum Zitat Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Math. Progr. 91, 201–213 (2002)CrossRefMATH Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Math. Progr. 91, 201–213 (2002)CrossRefMATH
11.
Zurück zum Zitat Gould, N.I.M., Orban, D., Sartenaer, A., Toint, PhL: Sentesivity of trust region algorithms to their parameters. A Q. J. Oper. Res. 3, 227–241 (2005)CrossRefMATHMathSciNet Gould, N.I.M., Orban, D., Sartenaer, A., Toint, PhL: Sentesivity of trust region algorithms to their parameters. A Q. J. Oper. Res. 3, 227–241 (2005)CrossRefMATHMathSciNet
12.
Zurück zum Zitat Li, D.H., Fukushima, M.: A modified BFGS method and its global convergence in nonconvex minimization. J. Comput. Appl. Math. 129, 15–35 (2001)CrossRefMATHMathSciNet Li, D.H., Fukushima, M.: A modified BFGS method and its global convergence in nonconvex minimization. J. Comput. Appl. Math. 129, 15–35 (2001)CrossRefMATHMathSciNet
13.
Zurück zum Zitat Lukšan L., Matonoha C., Vlček J.: Modified CUTE problems for sparse unconstrained optimization, Techical Report, NO. 1081, ICS AS CR, Nov (2010) Lukšan L., Matonoha C., Vlček J.: Modified CUTE problems for sparse unconstrained optimization, Techical Report, NO. 1081, ICS AS CR, Nov (2010)
14.
Zurück zum Zitat Lukšan, L., Vlček, J.: Sparse test problems for unconstrained optimization, Techical Report, NO. 1064, ICS AS CR, Nov (2003) Lukšan, L., Vlček, J.: Sparse test problems for unconstrained optimization, Techical Report, NO. 1064, ICS AS CR, Nov (2003)
15.
Zurück zum Zitat Kaufman, L.: Reduced storage, quasi-Newton trust region approaches to function optimization. SIAM J. Optim. 10(1), 56–69 (1999)CrossRefMATHMathSciNet Kaufman, L.: Reduced storage, quasi-Newton trust region approaches to function optimization. SIAM J. Optim. 10(1), 56–69 (1999)CrossRefMATHMathSciNet
16.
Zurück zum Zitat Powell, M.J.D.: Convergence properties of a class minimization algorithm. In: Mangasarian, O.L., Meyer, R.R., Robinson, S.M. (eds.) Nonlinear programming 2, pp. 1–27. Academic Press, New York (1975)CrossRef Powell, M.J.D.: Convergence properties of a class minimization algorithm. In: Mangasarian, O.L., Meyer, R.R., Robinson, S.M. (eds.) Nonlinear programming 2, pp. 1–27. Academic Press, New York (1975)CrossRef
17.
Zurück zum Zitat Rockafellar, R.T.: Convex analysis. Princeton University Press, Princeton (1970)MATH Rockafellar, R.T.: Convex analysis. Princeton University Press, Princeton (1970)MATH
18.
Zurück zum Zitat Nocedal, J., Wright, S.J.: Numerical optimization. Springer, New York (2006)MATH Nocedal, J., Wright, S.J.: Numerical optimization. Springer, New York (2006)MATH
19.
Zurück zum Zitat Nocedal, J., Yuan, Y.: Combining trust region and line search techniques. In: Yuan, Y. (ed.) Advanced in nonliear programming, pp. 153–175. Kluwer Academic Publishers, Dordrecht (1996) Nocedal, J., Yuan, Y.: Combining trust region and line search techniques. In: Yuan, Y. (ed.) Advanced in nonliear programming, pp. 153–175. Kluwer Academic Publishers, Dordrecht (1996)
20.
Zurück zum Zitat Sartenaer, A.: Automatic determination of an initial trust region in nonlinear programming. SIAM J. Sci. Comput. 18, 1788–1803 (1997)CrossRefMATHMathSciNet Sartenaer, A.: Automatic determination of an initial trust region in nonlinear programming. SIAM J. Sci. Comput. 18, 1788–1803 (1997)CrossRefMATHMathSciNet
22.
Zurück zum Zitat Simantiraki, E.M., Shanno, D.F.: An infeasible-interior-point method for linear complementarity problems. Siam J. Optim. 7, 620–640 (1997)CrossRefMATHMathSciNet Simantiraki, E.M., Shanno, D.F.: An infeasible-interior-point method for linear complementarity problems. Siam J. Optim. 7, 620–640 (1997)CrossRefMATHMathSciNet
23.
25.
Zurück zum Zitat Zarantonello, E.H.: Projections on convex sets in Hilbert space and spectral theory. In: Contributions to nonlinear functional analysis, Academic Press, 237–424 (1971) Zarantonello, E.H.: Projections on convex sets in Hilbert space and spectral theory. In: Contributions to nonlinear functional analysis, Academic Press, 237–424 (1971)
26.
Zurück zum Zitat Zhang, X.S., Zhang, J.L., Liao, L.Z.: An adaptive trust region method and its convergence. Sci. China 45, 620–631 (2002)MATHMathSciNet Zhang, X.S., Zhang, J.L., Liao, L.Z.: An adaptive trust region method and its convergence. Sci. China 45, 620–631 (2002)MATHMathSciNet
Metadaten
Titel
An efficient implementation of a trust region method for box constrained optimization
verfasst von
Hamid Esmaeili
Morteza Kimiaei
Publikationsdatum
01.06.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2015
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-014-0815-0

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