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Optimization in economy and statistics, convex analysis, introduction to non-linear programming, theory of linear
programming with respect to convex analysis and general optimization.
Supposed knowledge: Mathematical analysis (functions with several arguments, constraint extrema problems).
Last update: Zichová Jitka, RNDr., Dr. (02.05.2018)
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To give explanation and theoretical background for standard optimization procedures. Students will lern necessary theory and practice their knowladge on numerical examples. Last update: T_KPMS (14.05.2013)
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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 of a credit from exercises class are:
Last update: Branda Martin, doc. RNDr., Ph.D. (01.10.2021)
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Bazaraa, M.S.; Sherali, H.D.; Shetty, C.M.: Nonlinear programming: theory and algorithms. Wiley, New York, 1993.
Bertsekas, D.P.: Nonlinear programming. Athena Scientific, Belmont, 1999.
Dantzig, G.B.; Thapa, M.N.: Linear programming. 1,2. Springer, New York, 1997.
Luenberger, D.G.; Ye, Y.: Linear and Nonlinear Programming. 3rd edition, Springer, New York, 2008.
Plesník, J.; Dupačová, J.; Vlach, M.: Lineárne programovanie. Alfa, Bratislava, 1990.
Rockafellar, T.: Convex Analysis. Springer-Verlag, Berlin, 1975.
Rockafellar, T.; Wets, R. J.-B.: Variational Analysis. Springer-Verlag, Berlin, 1998.
Last update: T_KPMS (20.04.2015)
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Lecture + exercises. Last update: T_KPMS (14.05.2013)
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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 exercises class credit is necessary to sign up for the exam.
+--------------------------------------------------------------------------- Alternative requirements to exam in crisis situation +--------------------------------------------------------------------------- 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 specified by the course lecturer. The exercises class credit is necessary to sign up for the exam. Last update: Branda Martin, doc. RNDr., Ph.D. (01.10.2021)
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1. Optimization problems and their formulations.
2. Selected parts of convex analyses (convex cones, convex function, epigraph, subdifferential).
3. Separation theorems (Farkas theorem).
4. Theory of nonlinear programming. (Karush-Kuhn-Tucker optimality condition, constraints qualifications).
5. Linear a convex programming like a particular case of nonlinear programming.
6. Symmetric problem of nonlinear programming. Last update: Lachout Petr, doc. RNDr., CSc. (27.04.2018)
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introduction to optimization theory, convex analysis, functional analysis Last update: Lachout Petr, doc. RNDr., CSc. (30.05.2018)
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