Extended global convergence framework for unconstrained optimization

Acta Mathematica Sinica, English Series

Volumn 20, Issue 3, 2004, Pages 433-440

  Bűrmen, Árpád ^a   Bratković, Franc ^a   Puhan, Janez ^a   Fajfar, Iztok ^a   Tuma, Tadej ^a  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

Convergence analysis; Derivative free optimization; Descent methods; Grid based optimization

Indexed keywords

EID: 4744358546     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10114-004-0340-4     Document Type: Article

References (12)

1. Lewis, R. M., Torczon, V., Trosset, M. W.: Direct search methods: then and now. Journal of Computational and Applied Mathematics, (1-2), 191-207 (2000)
2. Wright, M. H.: Direct search methods: once scorned, now respectable, in Griffiths, D. F., Watson, G. A., Numerical Analysis 1995, Addison-Wesley Longman, Reading, MA, 191-208 (1996)
3. Powell, M. J. D.: Direct search algorithms for optimization calculations, Acta Numerica, 287-336 (1998)
4. Yu, W. C.: Positive basis and a class of direct search techniques. Scientia Sinica, Special Issue of Mathematics, 1, 53-67 (1979)
5. Torczon, V.: Multi-directional search: A direct search method for parallel machines, Ph. D. thesis, Department of Mathematical Sciences, Rice University, Houston, TX (1989)
6. Torczon, V.: On the convergence of pattern search algorithms. SIAM Journal on Optimization, 7, 1-25 (1997)
7. Lucidi, S., Sciandrone, M.: On the global convergence of derivative-free methods for unconstrained optimization. SIAM Journal on Optimization, 18, 97-116 (2002)
8. Grippo, L., Lampariello, F., Lucidi, S.: Global convergence and stabilization of unconstrained minimization methods without derivatives. Journal of Optimization Theory and Applications, 3, 385-406 (1988)
9. Coope, I. D., Price, C. J.: On the convergence of grid-based methods for unconstrained optimization. SIAM Journal on Optimization, 4, 859-869 (2001)
10. Coope, I. D., Price, C. J.: A direct search conjugate directions algorithm for unconstrained minimization, Tech. Rep. 188, Department of Mathematics & Statistics, University of Canterbury, Christchurch, New Zealand (1999)
11. Lewis, R. M., Torczon, V.: Rank ordering and positive bases in pattern search algorithms, Tech. Rep. 96-71, Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA (1996)
12. Davis, C.: Theory of positive linear dependence. American Journal of Mathematics, 83-108 (1954)