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Computational approaches to optimization problems. Algorithms for linear, nonlinear, integer and stochastic
programming problems. Branch and bound, cutting plane method. Lagrange duality, interior-point method, barrier
and penalty functions. Benders decomposition. Introduction to computational complexity. Optimization problems
with a special structure. Software tools for optimization.
Last update: T_KPMS (04.05.2015)
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Modern approaches to optimization are introduced. Real-life applications leading to linear, nonlinear, integer and stochastic programming problems are discussed. A special attention is paid to software tools (GAMS, Matlab etc.). Last update: T_KPMS (04.05.2015)
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The exercise class credit is necessary to sign up for the exam.
Requirements for exercise class credit: The credit for the exercise class will be awarded to the student who hands in a satisfactory solution to each of five assignments (4 standard and one final) by the prescribed deadline.
The nature of these requirements precludes any possibility of additional attempts to obtain the exercise class credit.
Last update: Branda Martin, doc. RNDr., Ph.D. (16.01.2024)
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Bazaraa, M.S., Sherali, H.D., Shetty, C.M. (2006): Nonlinear programming: theory and algorithms. Wiley, Singapore. Boyd, S., Vandenberghe, L. (2004): Convex Optimization, Cambridge University Press, Cambridge. Charamza, P. et. al. (1993): Modelling system GAMS, MFF UK, (in Czech). Kopa, M. et al. (2008): On Selected Software for Stochastic Programming, Matfyzpress, Prague. Nocedal, J., Wright, S.J. (2006): Numerical optimization. Springer, New York. Last update: Branda Martin, doc. RNDr., Ph.D. (06.01.2021)
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Lecture + exercises. Last update: T_KPMS (04.05.2015)
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The exam consists of two questions focused on the topics discussed during the lectures. The students must prove that they understand to the methods and algorithms and are able to apply them to examples. Last update: Zichová Jitka, RNDr., Dr. (05.03.2018)
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1. Dual simplex algorithm for LP. Wolfe algorithm for quadratic programming 2. Introduction to computational complexity 3. Integer linear programming - basic properties, branch-and-bound, cutting planes and Gomory cuts, vehicle routing problem, scheduling, lot-sizing, sparse optimization 4. Lagrange duality in nonlinear programming 5. Algorithms for nonlinear programming - quasi-Newton method, barier and penalty functions, interior point methods, SQP, alg. based on duality 6. Benders decomposition, L-shaped alg. 7. Minimax problems 8. Optimization problems with a special structure - semi-infinite, semi-definite and geometric prog., SOCP, DC, MPEC 9. Dynamic programming Last update: T_KPMS (04.05.2015)
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This course assumes knowledge of:
These topics are covered by Introduction to optimization (NMFM204), and Optimization theory (NMSA403). Last update: Zichová Jitka, RNDr., Dr. (01.05.2021)
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