Course is designed for senior undergraduate and graduate strudents in Math, Science, Engineering, and Mining
Prerequisite: Calculus, Linear Algebra, Familiarity with elementary programming.
Grade will be based on weekly homework, exams,  and class presentations. M 6870 strudents will be assigned an additional project.

Optimization

The desire for optimality (perfection) is inherent for humans. The search for extremes inspires mountaineers, scientists, mathematicians, and the rest of the human race.

 Search for  Perfection:  An image from  Bridgeman Art Library

A beautiful and practical optimization theory was developed from the sixties when computers become available. Every new generation of computers allowed for attacking new types of problems and called for new optimization methods. The aims are reliable methods to fast approach the extremum of a function of several variables by an intelligent arrangement of its evaluations (measurements). This theory is vitally important for modern engineering and planning that incorporate optimization at every step of the complicated decision making process.

This course discusses various direct methods, such as Gradient Method, Conjugate Gradients, Modified Newton Method, methods for constrained optimization, including Linear and Quadratic Programming, and others. We will also briefly review genetic algorithms that mimic evolution and stochastic algorithms that account for uncertainties of mathematical models. The course work includes several homework assignments that ask to implement the studied methods and a final project, that will be orally presented in the class.