Unconstrained and constrained global optimization using interval analysis

• Autorzy: Kubica B. , Niewiadomska-Szynkiewicz E.
• Języki publikacji: EN

Abstrakty

EN

This chapter presents techniques adressed to continuous, unconstrained and constrained optimization problems. Global optimization is defined as the problem of finding points on a bounded subset of X of Rn in which some real valued function f reaches its optimal (minimum or maximum) value. The algorithms considered are based on the branch-and-bound principles where the problem domain is partitioned iteratively. They apply interval arithmetic tools. The main objective is to discuss the advantages and disadvantages of existing algorithms and to provide some modifications for increasing their efficiency. The numerical results for several test problems are presented in the final part of the chapter.

Słowa kluczowe

EN

global unconstrained optimization; global constrained optimization; interval analysis; interval methods; branch-and-bound method

PL

optymalizacja globalna; analiza interwałowa; metoda interwałowa

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Prace Naukowe Politechniki Warszawskiej. Elektronika
• Rocznik: 2002
• Tom: z. 139
• Strony: 185--199
• Opis fizyczny: Bibliogr. 9 poz., tab., wykr.

Twórcy

autor

Kubica B.

• Institute of Control and Computation Engineering, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw

autor

Niewiadomska-Szynkiewicz E.

• Institute of Control and Computation Engineering, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw
• Research and Academic Computer Network (NASK), ul. Bartycka 18, 00-716 Warsaw

Bibliografia

• 1. Hansen E.: Global Optimization Using Interval Analysis – the multi-dimensional case, Numerische Mathematik, vol. 34, 1980, 247-270.
• 2. Hansen E.: Interval Forms of Newton Method, Computing, vol. 20, 1978, 153-163.
• 3. Hansen E.: An Interval Newton Method, Applied Mathematics and Computation, vol. 12, 1983, 89-98.
• 4. Horst R., Pardalos P.M.: Handbook of global optimization, Kluwer, 1995.
• 5. Kearfott R.B.: An interval branch and bound algorithm for bound constrained optimization problems, JOGO, vol. 2, 1992, 259-280.
• 6. Kearfott R.B.: On Verifying feasibility in equality constrained optimization problems, technical report 1996 available at http://interval.louisiana.edu/preprints.thml.
• 7. Markot M.C., Csendes T., Csallner A.E.: Multisection in interval branch- and- bound methods for global optimization II, Numerical Tests, JOGO, vol. 16, 1999, 219-228.
• 8. Ratshek H., Rokne J.G.: Efficiency of a global optimization algorithm, SIAM Journal of Numerical Analysis, vol. 5, 1987, 1191-1201.
• 9. Ratshek H., Voller R.L.: What can Interval Analysis Do for Global Optimization, JOGO, vol. 1, 1992, 111-130.