Syllabus
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
Annotation
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.