SE/EC 524/674 Optimization Theory and Methods
Working knowledge of Linear Algebra and some degree of mathematical maturity.
Introduction to optimization problems and algorithms emphasizing problem formulation, basic methodologies and the underlying mathematical structures. Covers the classical theory of linear and nonlinear optimization as well as recent advances in the field. Topics include: modeling issues, simplex method, duality theory, sensitivity analysis, large scale optimization, integer programming, interior-point methods, network optimization, nonlinear programming optimality conditions, Lagrange multipliers, and gradient methods. Applications of the theory and techniques developed in the course will be considered and a few case studies will be analyzed. Illustrative applications include: production planning and scheduling in manufacturing systems, fleet management, optimal routing in communication networks, and optimal portfolio selection.