COURSE AIMS AND OBJECTIVES: Understand the applications of, basic theoretical results, numerical methods for, and challenges in integer programming, network optimization and multiobjective optimization.
COURSE DESCRIPTION AND SYLLABUS:
Integer programming. Examples. The cutting-plane method and the branch-and-bound method.
Network optimization. Algorithmic approaches (with complexity considerations) for: Shortest path tree (Dijkstra; Bellman-Ford), Project planning and management (PERT-CPM), Maximum flow in a transportation network (Ford-Fulkerson and Edmonds-Karp algorithms), Weighted bipartite matching problem (Hungarian method), Transportation problem and minimum-cost network flow problem (network simplex method).
Multi-criteria optimization. Ideal and efficient (Pareto-optimal) points, dual characterizations of optimal points, weighted-sum method in multi-criteria programming, parametric simplex method for multi-objective linear programming, goal programming (reference point method and penalty weight method).
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