Linear and Nonlinear Optimization

Catalog description

This course provides an application-oriented introduction to linear programming and convex optimization, with a balanced combination of theory, algorithms, and numerical implementation. Theoretical topics will include linear programming, convexity, duality, and dynamic programming. Algorithmic topics will include the simplex method for linear programming, selected techniques for smooth multidimensional optimization, and stochastic gradient descent. Applications will be drawn from many areas, but will emphasize economics (eg two-person zero-sum games, matching and assignment problems, optimal resource allocation), data science (eg regression, sparse inverse problems, tuning of neural networks) and operations research (eg shortest paths in networks and optimization of network flows). While no prior experience in programming is expected, the required coursework will include numerical implementations, including some programming; students will be introduced to appropriate computational tools, with which they will gain experience as they do the assignments. | Prerequisites: A grade of C or better in ( MA-UY 2114 or MA-UY 2514 ) and ( MA-UY 1044 or MA-UY 2034 or MA-UY 3054 ).