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Course, academic year 2017/2018
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Fundamentals of Continuous Optimization - NMMB438
Czech title: Základy spojité optimalizace
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Is provided by: NOPT046
Guarantor: Andreas Emil Feldmann, Dr.
Class: M Mgr. MMIB
M Mgr. MMIB > Povinně volitelné
Classification: Mathematics > Optimization
Incompatibility : NOPT046
Interchangeability : NOPT046
Annotation -
Last update: G_I (11.04.2003)

Review course covering fundamental fields of optimization, incl. computational methods. There are countless examples from almost all branches of human doing leading to problems coming under this discipline. Introduction to several other courses specialized in the solution of particular classes of optimization problems.
Literature -
Last update: doc. Mgr. Milan Hladík, Ph.D. (04.05.2015)

M.S. Bazaraa, H.D. Sherali, C.M. Shetty: Nonlinear Programming, Wiley, New Jersey, 2006.

S. Boyd, L. Vandenberghe: Convex Optimization, Cambridge University Press, 2009.

W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver. Combinatorial Optimization. Wiley, New York, 1998.

Syllabus -
Last update: doc. Mgr. Milan Hladík, Ph.D. (07.04.2016)

Fundamentals of discrete optimization:

  • Introduction, examples of optimization examples and techniques. Analysis of algorithms, implementation and complexity.
  • Euler walk, greedy algorithms, shortest path and relations.
  • Maximum matching and applications, relation to flows in networks. Heuristics and algorithms for matchings (incl. probabilistic). Postman problem.
  • Traveling salesman problem (TSP): heuristics, applications and relations.
  • Comparisons of hard and polynomial algorithms: TSP, postman problem, Euler tours, minimal spanning tree, minimal Steiner tree.

Fundamentals of continuous optimization:

  • Convex functions and sets
  • Convex optimization
  • Quadratic programming
  • Cone programming and duality
  • Karush-Kuhn-Tucker optimality conditions
  • Basic methods
  • Programming with uncertain data, robust optimization

 
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