1. komponenta

Lecture type	Total
Lectures	45

COURSE AIMS AND OBJECTIVES: The aim of the course is to understand basic methods of convex optimization.

COURSE DESCRIPTION AND SYLLABUS:
1. Geometry of convex sets. Basic properties, extremal points, relative interior. Separation theorems, projection on convex set, support function.
2. Convex functions. Epigraph, slope function, sublinearity properties, subgradient. Duality between convex functions and convex sets.
3. Convex optimization. Lagrange function, KKT theorem (saddle form and gradient form). Duality theorem, mixed constraints, quadratic optimisation.

1. Nonlinear Programming: Theory and Algorithms, M. S. Bazaraa, H. D. Sherali, C. M. Shetty, John Wiley, 1993.
2. Convex Analysis and Nonlinear Optimization. Theory and Examples, J. Borwein, A. S. Lewis, Springer, 2006.
3. Introduction to the theory of nonlinear optimization, J. Jahn, Springer, 2007.
4. The Mathematics of Nonlinear Programming, A. L. Peressini, F. E. Sullivan, J. J. Uhl, Springer Verlag, 1993.
5. Convexity and Optimization in Banach Spaces, V. Barbu, T. Precupanu, Springer, 2012.
6. Convex analysis and monotone operator theory in Hilbert spaces, H. H. Bauschke, P. L. Combettes, Springer, 2011.
7. Convex Analysis and Minimization Algorithms, J -B. Hiriart-Urruty, C. Lemarechal, Springer Verlag, 1993.
8. Convexity & Optimization in Finite Dimensions I, J. Stoer, C. Witzgall, Springer Verlag, 1970.

Izborni modul Optimizacija - Regular study - Applied Mathematics

Izborni modul Optimizacija - Regular study - Applied Mathematics

Izborni modul Optimizacija - Regular study - Applied Mathematics

Izborni modul Optimizacija - Regular study - Applied Mathematics