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Lecturer(s)
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Tomeček Jan, doc. RNDr. Ph.D.
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Course content
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1. Convex sets and functionals. 2. Epigraphs and lower-semicontinuity. 3. Kernels of convex sets and the Minkowskii functional. 4. Continuity of convex functionals. 5. Ideal convex sets. 6. The Hahn-Banach theorem. 7. Basic principles of convex analysis. 8. Moreau-Rockefeller theorems. 9. Convex optimization. 10. Duality in convex programming. 11. Generalized convexity. 12. Asplund spaces.
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Learning activities and teaching methods
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Lecture, Work with Text (with Book, Textbook)
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Learning outcomes
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Apply subdifferential calculus of convex functions to convex optimization.
Application Apply subdifferential calculus of convex functions to convex optimization.
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Prerequisites
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Master's degree in mathematics.
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Assessment methods and criteria
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Oral exam, Dialog
Exam: the student has to understand the subject and be able to prove the principal results.
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Recommended literature
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J.-B. Hiriart-Urruty, C. Lemaréchal. (1993). Convex analysis and minimization algorithms I, II. Springer Verlag, Berlin.
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N. Hadjisavvas, S. Komlosi, S. Schaible (Eds.). (2005). Handbook on Generalized Convexity and Generalized Monotonicity. Springer, New York.
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O. Došlý. (2005). Základy konvexní analýzy a optimalizace v R^n. Brno.
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R. R. Phelps. (1993). Convex functions, Monotone operators and Differentiability. Berlin.
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R.T. Rockafellar. (1972). Convex Analysis. Princeton University Press, Princeton, New Jersey.
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