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Optimization in economy and in mathematical statistics.
Basis of convex analysis.
Theory of linear and nonlinear programming.
Symmetric nonlinear programming.
Supposed knowledge:
Linear algebra, functional analysis (functions with several arguments,
constraint extrema problems).
Last update: Omelka Marek, doc. Ing., Ph.D. (07.12.2020)
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To give explanation and theoretical background for standard optimization procedures. Students will learn necessary theory and practice their knowledge on numerical examples. Last update: Lachout Petr, doc. RNDr., CSc. (05.12.2020)
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+--------------------------------------------------------------------------- Course finalization +--------------------------------------------------------------------------- The course is finalized by a credit from the exercises class and exam. The exercises class credit is necessary to sign up for the exam.
Conditions for receiving credits from exercises class are available on the web page: https://www2.karlin.mff.cuni.cz/~branda/mbOpt11.html
Last update: Branda Martin, doc. RNDr., Ph.D. (02.10.2022)
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Bazaraa, M.S.; Sherali, H.D.; Shetty, C.M.: Nonlinear programming: theory and algorithms. Wiley, New York, 1993. Dantzig, G.B.; Thapa, M.N.: Linear programming. 1,2. Springer, New York, 1997. Plesník, J.; Dupačová, J.; Vlach, M.: Lineárne programovanie. Alfa, Bratislava, 1990. (in Czech) Rockafellar, T.: Convex Analysis. Springer-Verlag, Berlin, 1975.
Literatura pro další studium: Bertsekas, D.P.: Nonlinear programming. Athena Scientific, Belmont, 1999. Luenberger, D.G.; Ye, Y.: Linear and Nonlinear Programming. 3rd edition, Springer, New York, 2008. Rockafellar, T.; Wets, R. J.-B.: Variational Analysis. Springer-Verlag, Berlin, 1998. Last update: Lachout Petr, doc. RNDr., CSc. (05.12.2020)
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Lecture + exercises. Last update: Omelka Marek, doc. Ing., Ph.D. (30.11.2020)
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+--------------------------------------------------------------------------- Requirements to exam +--------------------------------------------------------------------------- The exam is contained from a written part and an oral part. Written part is foregoing to oral part. If written part is not fulfilled, whole exam is marked as non-satisfactory, and oral part is not treated. Mark from the examination is determined considering results from both written and oral part. If student did not pass the exam, he must repeat both written part and oral part next time. Examination is checking knowledge of all topics read at the lecture and parts given to self-study by the course lecturer. The practical class credit is necessary to sign up for the exam.
Conditions for receiving of a credit from practical class are:
Last update: Lachout Petr, doc. RNDr., CSc. (14.02.2024)
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1. Optimization problems and their formulations. Applications in economy and in mathematical statistics. 2. Selected parts of convex analyses (convex sets, convex cones, extreme points, extreme directions). 3. Selected parts of functional theory. Differentiation in Peano sense. Convex functions with several variables (epigraph, subgradient, subdiferential). 4. Separation theorems (Farkas theorem). 5. Theory of linear programming (structure of the set of all feasible solutions, basic theorem of linear programming, duality). 6. Direct method for solving linear programming, simplex method, dual simplex method, postoptimization. 7. Theory of nonlinear programming (saddle point condition, Karush-Kuhn-Tucker optimality conditions, constraint qualifications). 8. Symmetric nonlinear programming. 9. Linear and convex programming as a particular case of nonlinear programming. 10. Transport problem as a particular case of linear programming. 11. Main ideas of algorithms for nonlinear programming. 12. Matrix games and linear programming, minimax theorem. Last update: Lachout Petr, doc. RNDr., CSc. (05.12.2020)
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Linear algebra, functional analysis. Last update: Lachout Petr, doc. RNDr., CSc. (05.12.2020)
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