Methods of optimization M- 7710

Three credit hours.  The class meets Monday, Wednesday at 3:00 - 4:15

Instructor:  Professor Andrej Cherkaev Department of Mathematics  Office: JWB 225  Email: cherk@math.utah.edu Tel : +1 801 - 581 6822 The class meets Monday, Wednesday at 3:00 - 4:15

Three credit hours.  The class meets Monday, Wednesday at 3:00 - 4:15

A. Description.

The course discusses practical methods that are in high demand in industry and research planning,  teaches modelling in relation of optimization, and variational methods.

The desire for optimality (perfection) is inherent for humans. A beautiful and practical mathematical theory of optimization is developed since the sixties when computers become available. This theory is vitally important for modern engineering and planning that incorporate optimization at every step of the complicated decision making process. The modern variational branch of the theory allows for optimal design, including structural optimization.

B. Content

1. Extremum of a function of one variable Fibbonacci and Golden Mean method, Secant method, Newton method. Modeling and Optimization
2.  Gradient search, Newton method and its modifications, Conjugate Gradient method. Constrained optimization
3. Linear Programming. Quadratic programming. Convex programming. Review of various methods (Stochastic search, Genetic algorithms)
4. Minimax and introduction to games.
5. Calculus of variation. First variations and inequality conditions for local minimum
6. Mutivariable problems of calculus of variations.
7. Ritz and Galerkin-type methods
8. Design of sources, optimization of domains, design of material properties.

C. The course is addressed to seniors, master and PhD students in math, science, and engineering.

D. Prerequisit: Engineering math series: Calculus, ODE. PDE, numerical methods.