Piecewise partially separable functions and a derivative-free algorithm for large scale nonsmooth optimization

Journal of Global Optimization

Volumn 35, Issue 2, 2006, Pages 163-195

  Bagirov, Adil M ^a   Ugon, Julien ^a  

^a UNIVERSITY OF BALLARAT   (Australia)

Author keywords

Discrete gradient; Large scale optimization; Nonsmooth optimization; Piecewise partially separable functions; Subdifferential

Indexed keywords

ALGORITHMS; FUNCTIONS; NUMERICAL ANALYSIS; PROBLEM SOLVING;

DISCRETE GRADIENT; LARGE SCALE OPTIMIZATION; NONSMOOTH OPTIMIZATION; PIECEWISE PARTIALLY SEPARABLE FUNCTIONS; SUBDIFFERENTIAL;

OPTIMIZATION;

EID: 33745446251     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-005-3834-4     Document Type: Article

References (27)

1. Aberick, B.M., Bicshof, C.H., Carle, A., More, J. and Griewank, A. (1994), Computing large sparse Jacobian matrices using automatic differentiation, SIAM Journal on Scientific and Statistical Computing 15, 285-294.
2. Bagirov, A.M. and Gasanov, A.A. (1995), A method of approximating a quasidifferential, Russian Journal of Computational Mathematics and Mathematical Physics 35(4), 403-409.
3. Bagirov, A.M. (1999), Minimization methods for one class of nonsmooth functions and calculation of semi-equilibrium prices, In: Eberhard, A. et al. (eds.) Progress in Optimization: Contribution from Australasia, Kluwer Academic Publishers, pp. 147-175.
4. Bagirov, A.M. (2002), A method for minimzation of quasidifferentiable functions, Optimization Methods and Software 17(1), 31-60.
5. Bagirov, A.M. (2003), Continuous subdifferential approximations and their applications, Journal of Mathematical Sciences 115(5), 2567-2609.
6. Bagirov, A.M., Rubinov, A.M., Soukhoroukova, N.V. and Yearwood, J. (2003), Unsupervised and supervised data classification via nonsmooth and global optimization, TOP: Spanish Journal of Operations Research 1-93.
7. Bagirov, A.M. and Ugon, J. (2005), An algorithm for minimizing clustering functions, Optimization 54(4-5), 351-368.
8. Bagirov, A.M. Max-min separability, Optmization Methods and Software 20(2-3), 271-290.
9. Bagirov, A.M. and Yearwood, J. A new nonsmooth optimization algorithm for minimum sum-of-squares clustering problems, European Journal of Operational Research 170(2), 578-596.
10. Bock, H.H. (1974), Automatische Klassifikation, Vandenhoeck & Ruprecht, Gottingen.
11. Clarke, F.H. (1983), Optimization and Nonsmooth Analysis, Wiley, New York.
12. Colson, B. and Toint, Ph.L. (2002), A derivative-free algorithm for sparse unconstrained optimization problems, In: Siddiqi, A.H., and Kocvara, M. (eds.), Trends in Industrial and Applied Mathematics, Kluwer Academic Publishers, Dordrecht, pp. 131-147.
13. Conn, A.R., Gould, N. and Toint, Ph.L. (1994), Improving the decomposition of partially separable functions in the context of large-scale optimization: a first approach, In: Hager, W.W., Hearn, D.W., and Pardalos, P.M. (eds.), Large Scale Optimization: State of the Art, Kluwer Academic Publishers, Dordrecht, pp. 82-94.
14. Demyanov, V.F. and Rubinov, A.M. (1995), Constructive Nonsmooth Analysis, Peter Lang, Frankfurt am Main.
15. Evtushenko, Yu.G. (1972), A numerical method for finding best guaranteed estimates, USSR Journal of Computational Mathematics and Mathematical Physics 12, 109-128.
16. Griewank, A. and Toint, Ph.L. (1982), On the unconstrained optimization of partially separable functions, In: Powell, M.J.D. (ed.), Nonlinear Optimization, Academic Press, pp. 301-312.
17. Haarala, M., Miettinen, K. and Makela, M.M. (2004), New-limited memory bundle method for large-scale nonsmooth optimization, Optimization Methods and Software 19(6), 673-692.
18. Hansen, P. and Jaumard, B. (1997), Cluster analysis and mathematical programming, Mathematical Programming 79(1-3), 191-215.
19. Hiriart-Urruty, J.-P. and Lemarechal, C. (1993), Convex Analysis and Minimization Algorithms, Vol. 1 and 2, Springer-Verlag, Berlin, New York.
20. Kiwiel, K.C. (1985), Methods of Descent for Nondifferentiable Optimization, Lecture Notes in Mathematics, 1133, Springer-Verlag, Berlin.
21. Jain, A.K., Murty, M.N. and Flynn, P.J. (1999), Data clustering: a review, ACM Computing Surveys 31(3), 264-323.
22. Luksan, L. and Vlcek, J. (1999), Sparse and partially separable test problems for unconstrained and equality constrained optimization, Technical Report 767, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague.
23. Luksan, L. and Vlcek, J. (2000), Test problems for nonsmooth unconstrained and linearly constrained optimization, Technical Report 798, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague.
24. Makela, M.M. and Neittaanmaki, P. (1992), Nonsmooth Optimization, World Scientific, Singapore.
25. Mifflin, R. (1977), Semismooth and semiconvex functions in constrained optimization, SIAM Journal on Control and Optimization 15(6), 959-972.
26. Nelder, J.A. and Mead, R. (1965), A simplex method for function minimization, Computer Journal 7, 308-313.
27. Powell, M.J.D. (2002), UOBYQA: unconstrained optimization by quadratic approximation, Mathematical Programming Series B, 92(3), 555-582.