Интервальный анализ

и его приложения

20:49    Четверг    18 Апрель 2024

Интервальные методы для глобальной оптимизации функций

С.П. Шарый
Рандомизированные алгоритмы в интервальной глобальной оптимизации // Сибирский Журнал Вычислительной математики. – 2008. – Том 11, №4. – С. 457-474.

С.П. Шарый
Новый подход в интервальной глобальной оптимизации // Труды XII Байкальской международной конференции «Методы оптимизации и их приложения», Иркутск, Байкал, 24 июня–1 июля 2001 года. Том 1 «Математическое программирование». – Иркутск: ИСЭМ СО РАН, 2001. – С. 289-295.

S. Berner
Parallel methods for verified global optimization practice and theory // Journal of Global Optimization. – 1996. – Vol. 9. – P. 1-22.

T. Csendes
Generalized subinterval selection criteria for interval global optimization // Numerical Algorithms. – 2004. – Vol. 37. – P. 93-100.

E.R. Hansen
Global optimization using interval analysis: the one-dimensional case // Journal of Optimization Theory and Applications. – 1979. – Vol. 29, No. 3. – P. 331-344.

E.R. Hansen
Global optimization using interval analysis: the multidimensional case // Numerische Mathematik. – 1980. – Vol. 34. – P. 247-270.

K. Ichida, Y. Fujii
Multicriterion optimization using interval analysis // Computing. – 1990. – Vol. 44. – P. 47-57.

R.B. Kearfott, V. Kreinovich
Beyond convex? Global optimization is feasible only for convex objective functions // Journal of Global Optimization. – 2005. – Vol. 33. – P. 617-624.

R.B. Kearfott, G.W. Walster
On stopping criteria in verified nonlinear systems or optimization algorithms // ACM Transactions on Mathematical Software. – 2000. – Vol. 26, No. 3. – P. 373-389.

H. Munack
On global optimization using interval analysis // Computing. – 1992. – Vol. 48. – P. 319-336.

P.S.V. Nataraj, K. Kotecha
An algorithm for global optimization using the Taylor-Bernstein form as inclusion function // A manuscript. – 2004.

A. Neumaier
Complete search in continuous global optimization and constraint satisfation // Acta Numerica. – 2004. – 94 p.

K. Nickel
Optimization using interval mathematics // Freiburger Intervall-Berichte. – 1986. – #86/7. – P. 55-83

J.A. Martínez, L.G. Casado, I. García, Ya.D. Sergeyev, B. Tóth
On an efficient use of gradient information for accelerating interval global optimization algorithms // Numerical Algorithms. – 2004. – Vol. 37. – P. 61-69.

I.B. Mohd
Computable error bounds for an optimization problem with parallelepiped constraint // Journal of Computational and Applied Mathematics. – 1995. – Vol. 58. – P. 183-192.

D. Oelschlägel, H. Süsse
Interval analytic treatment of convex programming problems // Computing. – 1980. – Vol. 24. – P. 213-225.

H. Ratschek, R.L. Voller
What can interval analysis do for global optimization? // Journal of Global Optimization. – 1991. – Vol. 1. – P. 111-130.

H. Schichl, A. Neumaier
Interval analysis on directed acyclic graphs for global optimization // Journal of Global Optimization. – 2005. – Vol. 33. – P. 541-562.

Z. Shen, Y. Zhu
An interval version of Shubert's iterative method for the localization of the global maximum // Computing. – 1987. – Vol. 38. – P. 275-280.

Sergey P. Shary
A surprising approach in interval global optimization // Reliable Computing. – 2001. – Vol. 7. – P. 497-505.

Sergey P. Shary
Randomized algorithms in interval global optimization // Numerical Analysis and Applications. – 2008. – Vol. 1, No. 4. – P. 376-389.

T. Vinkó, D. Ratz
A multidimensional branch-and-prune method for interval global optimization // Numerical Algorithms. – 2004. – Vol. 37. – P. 391-399.