Cutting angle method - A tool for constrained global optimization

Optimization Methods and Software

Volumn 19, Issue 2, 2004, Pages 137-151

  Beliakov, Gleb ^a  

^a DEAKIN UNIVERSITY   (Australia)

Author keywords

Global optimization; Lipschitz optimization; Saw tooth underestimate

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER AIDED MANUFACTURING; CONSTRAINT THEORY; FUNCTIONS; GLOBAL OPTIMIZATION; LINEAR EQUATIONS; LINEAR PROGRAMMING; MATHEMATICAL MODELS; SOFTWARE ENGINEERING;

LIPSCHITIZ OPTIMIZATION; SAW-TOOTH UNDERESTIMATES;

INFORMATION TECHNOLOGY;

EID: 1842664459     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/10556780410001647177     Document Type: Article

References (15)

1. M. Andramonov, A. Rubinov and B. Glover (1999). Cutting angle methods in global optimization. Appl. Math. Lett., 12(3), 95-100.
2. A.M. Rubinov (2000). Abstract Convexity and Global Optimization. Nonconvex Optimization and its Applications, Vol. 44. Kluwer Academic Publishers, Dordrecht, Boston.
3. P. Hansen and B. Jaumard (1995). Lipschitz optimization. In: Reiner Horst and P. Pardalos (Eds.), Handbook of Global Optimization, pp. 407-493. Kluwer, Dordrecht.
4. S.A. Pijavski (1972). An algorithm for finding the absolute extremum of a function. USSR Comput. Math. And Math. Phys., 2, 57-67.
5. B. Shubert (1972). A sequential method seeking the global maximum of a function. SIAM J. Numer. Anal., 9, 379-388.
6. R.G. Strongin and Y.D. Sergeyev (2000). Global Optimization with Non-Convex Constraints: Sequential and Parallel Algorithms. Nonconvex Optimization and its Applications, Vol. 45. Kluwer Academic Publishers, Dordrecht, London.
7. J.E. Kelley (1960). The cutting-plane method for solving convex programs. J. SIAM, 8, 703-712.
8. A. Bagirov and A. Rubinov (2001). Modified versions of the cutting angle method. In: N. Hadjisavvas and P.M. Pardalos (Eds.), Convex Analysis and Global Optimization. Nonconvex Optimization and its Applications, Vol. 54, pp. 245-268. Kluwer, Dordrecht.
9. A. Bagirov and A. Rubinov (2000). Global minimization of increasing positively homogeneous function over the unit simplex. Ann. Oper. Res., 98, 171-187.
10. L.M. Batten and G. Beliakov (2002). Fast algorithm for the cutting angle method of global optimization. J. Global Optim., 24, 149-161.
11. R. Horst, P. Pardalos and N. Thoai (2000). Introduction to Global Optimization, 2nd ed. Kluwer Academic Publishers, Dordrecht.
12. R. Mladineo (1986). An algorithm for finding the global maximum of a multimodal, multivariate function. Math. Progr., 34, 188-200.
13. G. Beliakov (2003). Geometry and combinatorics of the cutting angle method. Optimization, 52, 379-394.
14. K.F. Lim, G. Beliakov and L.M. Batten (2003). Predicting molecular structures: application of the cutting angle method. Phys. Chem. Chem. Phys., 5, 3884-3890.
15. C.A. Floudas (2000). Deterministic Global Optimization: Theory, Methods, and Applications. Nonconvex Optimization and its Applications, Vol. 37. Kluwer Academic Publishers, Dordrecht, London.