Graduate Courses

Part A: Mathematical Programming. Modelling in decision making; introduction to linear programming; applications of linear programming in marketing, finance, business administration and related case studies; the Simplex algorithm; sensitivity analysis; duality theory; parametric analysis of linear-programming solutions; other solution algorithms; the transportation problem and its main variants, including transshipment and assignment problems. Optimization models for network analysis, such as shortest path, spanning tree, maximum flow, minimum-cost flow, PERT/CPM project scheduling and the network Simplex method. Multi-criteria linear programming, goal programming and Data Envelopment Analysis. Applications, model flexibility using binary variables, branch-and-bound, feasible-region restriction methods such as Gomory cuts. Basic features of dynamic-programming problems and mathematical formulation of the methodology, including shortest path, tool replacement, resource allocation, optimal loading, travelling salesman, and economic order quantity models and variants. Expected utility theory, game representation, strategies, Nash equilibrium in simultaneous, extensive, repeated and stochastic games, bargaining, auctions, evolutionary game theory, psychological game theory and algorithmic game theory. Part B: Numerical methods for unconstrained nonlinear optimization. Mathematical formulation of nonlinear optimization, method categories, local and global optima, mathematical background, the no-free-lunch theorem for optimization, optimality conditions, iterative procedures and termination criteria. Line-search methods, exact and inexact step-length strategies, Armijo, curvature, Wolfe, strong Wolfe and Goldstein conditions, backtracking line search, steepest descent, Newton, line-search Newton, conjugate-gradient and quasi-Newton methods, with applications.