Responsible lecturer: Tibor Csendes, university professor (csendes@inf.u-szeged.hu)
Assumed preliminary studies:
Linear and Nonlinear Programming
Topics:
- Different forms of global optimization problems, computational complexity, computational complexity relative to the complexity of linear programming.
- Problem transformation, transformation to single variable problem
- Classification of global optimization problems, classification according to the information applied.
- Grid search, random search, dependency on the dimensions of the problem, simulated annealing, genetic, evolutionary, and neural network based methods, their theoretical background.
- Stochastic and multistart methods for global optimization, their speeds of convergences and stopping conditions.
- Known Lipschitz constant based methods, convergence theorem, single and multi dimensional algorithms.
- DC functions, their properties and applications in solving global optimization problems.
- Effective solutions for special structure (concave, bilinear, etc.) problems, outer approximation and cut methods.
- Interval arithmetic, interval division methods, acceleration tool, interval Newton method, speed of convergence.
- Patological problems, symbolic manipulation for global optimization, practical applications, case studies
Required* and proposed literature:
Strongin, R.G.: Numerical Methods in Multiextremal Optimization, Nauka, Moscow, 1978 (in Russian).
Dixon, L.C.W., G.P. Szegő (eds.): Towards global optimisation, North-Holland, Amsterdam, 1975.
Dixon, L.C.W., G.P. Szegő (eds.): Towards global optimisation 2, North-Holland, Amsterdam, 1978.
Wilde, D.J.: Globally optimal design. Wiley, New York, 1978.
Dixon, L.C.W., E. Spedicato, G.P. Szegő: Nonlinear Optimization Theory and Algorithms. Birkhä user, Boston, 1980.
Zilinskas, A.: Global Optimization - Axiomatics of Statistical Models, Algorithms and Their Application, Mokslas, Vilnius, 1986 (in Russian).
Pardalos, P.M., J.B. Rosen: Constrained Global Optimization: Algorithms and Applications. Springer-Verlag, Lecture Notes in Computer Science Vol. 268, Berlin, 1987.
Törn, A., A. Zilinskas: Global Optimization, Springer-Verlag, Lecture Notes in Computer Science Vol. 350, Berlin, 1987.*
Ratschek, H., J. Rokne: New computer methods for global optimization, Ellis Horwood, Chichester, 1988.*
Mockus, J.: Bayesian Approach to Global Optimization, Kluwer, Dordrecht, 1989.
Nemhauser, G.L., A.H.G. Rinnooy Kan, M.J. Todd: Optimization, Handbooks in Operations Research and Management Science Vol. 1, North-Holland, Amsterdam, 1989.
Horst, R., H. Tuy: Global Optimization - Deterministic Approaches, Springer-Verlag, Berlin, 1990.*
Floudas, C.A., P.M. Pardalos: A collection of test problems for constrained global optimization algorithms. Lecture Notes in Computer Science Vol. 455. Springer-Verlag, Berlin, 1990.
Zhigljavsky, A.A.: Theory of Global Random Search, Kluwer, Dordrecht, 1991.
Floudas, C.A., P.M. Pardalos: Recent Advances in Global Optimization, Princeton University Press, Princeton, 1992.
Hansen, E.: Global optimization using interval analysis, Marcel Dekker, New York, 1992.
Horst, R., P.M. Pardalos: Handbook of Global Optimization, Kluwer, Dordrecht, 1995.*
Horst, R., P.M. Pardalos, N.V. Thoai: An Introduction to Global Optimization, Kluwer, Dordrecht, 1995.*