Optimal covering of plane domains by circles via hyperbolic smoothing

Journal of Global Optimization

Volumn 31, Issue 3, 2005, Pages 493-504

  Xavier, Adilson Elias ^a   De Oliveira, Antonio Alberto Fernandes ^a  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Location problems; Min max min problems; Non differentiable programming; Smoothing

Indexed keywords

CRYSTALLOGRAPHY; MATHEMATICAL MODELS; MATHEMATICAL PROGRAMMING; TELECOMMUNICATION SYSTEMS;

LOCATION PROBLEMS; MIN-MAX-MIN PROBLEMS; NON-DIFFERENTIABLE PROGRAMMING; SMOOTHING;

PROBLEM SOLVING;

EID: 22944477687     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10898-004-0737-8     Document Type: Article

References (19)

1. Bertsekas, D.P. (1982), Constrained Optimization and Lagrange Multiplier Methods, San Diego, Academic Press.
2. Chaves, A.M.V. (1997), Resolução do Problema Minimax Via Suavização, M.Sc. Thesis - COPPE - UFRJ, Rio de Janeiro.
3. Conway, J.H. and Sloane, N.J.A. (1988), Sphere Packings, Lattices and Croups, Springer, New York.
4. Demyanov, V.F. (1971), On the Maximization of a Certain Nondiffererentiable Function. Journal of Optimization Theory and Applications 7(2), 75-89.
5. Du, D.Z. and Pardalos, P.M. (ed.), (1995), Minimax and Applications, Kluwer Academic Publishers.
6. Galiyev, S. (1995), Computational algorithms for the optimum covering plane domains by a prescribed number of ellipses. Computational Mathematics and Mathematical Physics 35(5), 609-617.
7. Galiyev, S. (1997), Finding approximate solutions to minimax problems, Computational Mathematics and Mathematical Physics 37(12), 1439-1448.
8. Hales, T.C. (1992), The sphere packing problem. Journal of Computational and Applied Mathematics, 44, 41-76.
9. Maranas, C., Floudas, C. and Pardalos, P.M. (1995), New results in the packing of equal circles in a square. Discrete Mathematics 142, 287-293.
10. Oliveira, A.A.F. (1979), Recobrimento Continuo Ótirno, D.Sc. Thesis-COPPE-UFRJ, Rio de Janeiro.
11. Pillo, Grippo, and Lucidi, (1993), A smooth method for the finite minimax problem. Mathematical Programming 60, 187-214.
12. Pinar and Zenios, (1994), On smoothing exact penalty functions for convex constrained optimization. SIAM Journal Optimization 4, 486-511.
13. Polyak, R.A. (1988), Smooth optimization methods for minimax problems. SIAM Journal on Control and Optimization 26, 1274-1286.
14. Rogers, C.A. (1964), Packing and Covering Cambridge University Press, Cambridge.
15. Santos, A.B.A. (1997), Problemas de Programação Não- Diferenciável: Uma Metodologia de Suavização, M.Sc. Thesis - COPPE - UFRJ, Rio de Janeiro.
16. Toth, L.F. (1964), Regular Figures, Pergamon Press, New York.
17. Toth, L.F. (1983), New results in the theory of packing and covering. In: Convexity and its Applications, pp. 312-359. Birkhauser, Basel.
18. Xavier, A.E. (1982), Penalizaçáo Hiperbólica: Um Novo Método para Resolução de Problemas de Otimização, M.Sc. Thesis - COPPE - UFRJ, Rio de Janeiro.
19. Xavier, A.E. (2000), Optimum covering of plane domains by circles. International Symposium of Mathematical Programming, Atlanta August 2000.