Course Descriptions - Operations Research/Optimization
550.461* Optimization Methods in Finance: Optimization methods motivated by financial applications. Linear and nonlinear programming, integer programming, dynamic programming, stochastic programming, and robust methods. Applications will include portfolio optimization, volatility modeling, immunization, identification of arbitrage, and index fund construction.
550.661 Foundations of Optimization: Study of the fundamental theory underlying linear and nonlinear optimization. Unconstrained optimization, constrained optimization, saddlepoint conditions, Kuhn-Tucker conditions, linear programming, the simplex algorithm, post-optimality, duality, convexity, quadratic programming. Prerequisites: multivariable calculus, linear algebra. Corequisite: 110.405.
550.662 Optimization Algorithms: Design and analysis of algorithms for linear and nonlinear optimization. The revised simplex method, the primal-dual algorithm, algorithms for network problems, first- and second-order methods for nonlinear problems, quadratic programming techniques, and methods for constrained nonlinear problems. Prerequisite: 550.661.
550.663 Stochastic Search and Optimization: An introduction to stochastic search and optimization, including discrete and continuous optimization problems. Topics will include the “no free lunch” theorems, beneficial effects of injected Monte Carlo randomness, algorithms for global and local optimization problems, random search, recursive least squares, stochastic approximation, simulated annealing, evolutionary and genetic algorithms, machine (reinforcement) learning, and statistical multiple comparisons. Prerequisites: graduate course in probability and statistics and knowledge of basic matrix algebra.
550.761 Advanced Linear Programming: Further theory and applications of optimizing a linear function subject to linear constraints. An advanced algorithmic or theoretical topic (for example, nonsimplex methods), and/or an advanced modeling or application topic (for example, the use of linear programming in treating Markov decision chains, or stochastic programming) are studied in depth. Prerequisite: 550.661.
550.762 Advanced Nonlinear Programming: Theory and applications of optimizing a nonlinear function subject to linear or nonlinear constraints. Duality theory, convex analysis, and nonlinear sensitivity analysis; applications of these techniques to special classes of problems such as geometric programs and location problems. Prerequisites: 110.405, 550.661.
550.764 Optimization of Functionals: Examination from a unified point of view of topics in infinite-dimensional optimization such as the calculus of variations, optimal control theory, and approximation theory. Applications in the physical sciences, engineering, and statistics. Prerequisites: 110.405, 550.661.
550.765 Numerical Methods for Optimization: Advanced topics in the design and analysis of numerical methods for solving optimization problems. Algorithms include gradient methods, conjugate direction techniques, quasi-Newton methods, feasible direction methods, and successive quadratic programming. Issues of matrix factorization and updating, data storage, line searches, convergence, efficiency, and numerical stability. Prerequisites: 550.662, 550.681.