MU24006 Optimization Methods in Practice

Mathematical Institute in Opava
Summer 2019
Extent and Intensity
2/1/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
RNDr. Oldřich Stolín, Ph.D.
Mathematical Institute in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
1. Introduction: Modeling and optimization. Types of problems and methods, examples. Assignment of semester projects. 2. Extrema of functions of one varriable. Fibonacci method and golden section search. Secant method. Newton's method. 3. Optimization without constraints: gradient methods, Newton's method and its variants, the method of the conjugate gradient, quasi-Newton methods, comparative methods. 4. Optimization with constraints: Nonconvex and convex problems, method of Lagrange multipliers and generaliizations, penalization and barrier methods, method of projection and reduction of the gradient. 5. Linear, quadratic, and nonlinear programming. Linear problems with special structure. Duality. 6. Further practical methods: Stochastic methods, genetic algorithms, discrete methods.
Syllabus
  • Extremal problems.
    Lagrange multipliers, the Kuhn-Tucker theorem.
    Classical variational calculus.
    The instruments of the theory of extremal problems.
    The Lagrange principle for smooth bounded problems.
    Optimal control.
Literature
    recommended literature
  • J. W. Chinneck. Practical Optimization: A Gentle Introduction. URL info
  • Topics in Applied Math: Methods of Optimization. URL info
  • V. M. Alexejev, S. V. Fomin, V. M. Tichomirov. Matematická teorie optimálních procesů. Academia, Praha, 1991. ISBN 80-200-0319-3. info
  • P. E. Gill, W. Murray, M. H. Wright. Practical optimalization. Academic Press, London and New York, 1981. info
    not specified
  • Optimization Tree. URL info
  • N. A. Thacker, T. F. Cootes. Vision Through Optimalization. URL info
  • M. Maňas. Optimalizační metody. SNTL, Praha, 1991. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2009, Winter 2010, Winter 2011, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018.
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