Course syllabus for Large scale optimization

• independently analyze and suggest modelling and solution principles for large-scale complex optimization problems;
• have sufficient knowledge to use these principles successfully in practice through the use of computation software for optimization problems.

Large-scale optimization problems often possess some inherent structures that can be exploited in order to solve such problems efficiently. The course deals with a number of such principles through which large-scale optimization problems can be attacked. A common term for such techniques is decomposition–coordination (or, distributed algorithm–consensus); convexity and duality theory underlie its development. The course includes practical moments: exercises in the modelling and solution of optimization problems with complicating constraints and/or variables, and project assignments in which large-scale optimization problems are to be solved through the use of duality theory and techniques presented during the lectures. 

Contents in brief: complexity, simple/difficult optimization problems, integer linear optimization problems, unimodularity, convexity. Decomposition–coordination, restriction, relaxation, bounds on the optimal value, projection, variable fixing, dualization, neighbourhoods, heuristics, local search methods. Lagrangean duality, subgradient methods, (ergodic) convergence, recovery of integer solutions, Lagrangean heuristics, cutting planes, column generation, coordinating master problem, Dantzig–Wolfe decomposition, Benders decomposition.

Lectures. Modelling exercises including oral presentations and discussions. Project assignments including oral and written presentations as well as oppositions. Advisement. Mandatory presence at workshops.

See the course home page.

Written reports and oral presentations of the projects, which may also give bonus points on the exam; opposition/peer review; presence and active participation at workshops; a written exam.