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Thesis topic proposal
 
Tibor Csendes
Development and application of reliable global optimization algorithms

THESIS TOPIC PROPOSAL

Institute: University of Szeged
computer sciences
PhD School in Computer Science

Thesis supervisor: Tibor Csendes
Location of studies (in Hungarian): SZTE
Abbreviation of location of studies: SZTE


Description of the research topic:

Global optimization problems nowadays occur in any area of science, most of which are problems where an accurate, guaranteed optimum is needed. At this time, the problem must be solved by means of reliable global optimization algorithms, which may vary depending on the properties of the problem. These algorithms, however, are all the same: all parts of the search space are examined and only those subproblems are not considered for further study that have been proven to have no global optimum.

The student needs to know the various global optimization algorithms that can provide a guaranteed solution focusing on Branch-and-Bound algorithms that find the global optimum by bounding the objective function of the problem. The diversity of methods is given here by the various modes of bounding the objective functions. There are general strategies such as interval analysis and Lipschitz optimization that under certain conditions can be used for a variety of objective functions without the knowledge of their particular properties. Another choice is to construct specific lower and upper bound functions, using for instance D.C. decomposition, if it can be specified, or using other methods to bound the objective function with convex functions.

The student's task is to improve these methods and, if necessary, to develop new algorithms for one or more applications. Such applications may be a facility location problem or a non-linear nonconvex problem from technical science with small dimension. Testing the algorithms can be carried out on the test problems found in the literature or on given real-life problems, if they are known.

Literature:
R. Horst, P.M. Pardalos (editors): Handbook of Global Optimization, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995.
Eligius M.T. Hendrix and B. G.-Tóth: Introduction to Global and Nonlinear Optimization, Springer, New York, 2010.
Laporte, Gilbert, Nickel, Stefan, Saldanha da Gama, Francisco (Eds.): Location Science, New York; Dordrecht: Springer, 2015.

Required language skills: English
Further requirements: 
operations research, programming skills

Number of students who can be accepted: 1

Deadline for application: 2019-03-15

 
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