Methods of optimization  M- 7710

Three credit hours. 
The class meets Monday, Wednesday at 3:00 - 4:15 in LCB 225




Instructor: 
Professor Andrej Cherkaev

Department of Mathematics 
Office: JWB 225 
Email: cherk@math.utah.edu
Tel : +1 801 - 581 6822




A. Description. 

Methods of optimization  discusses practical methods of optimization that are in high demand in industry and research planning,  teaches modeling in relation of optimization, and reviews the state of arts in optimization.The variational branch of the theory allows for optimal design, including structural optimization.

The desire for optimality is inherent for humans. A beautiful and practical mathematical theory of optimization is vitally important for modern engineering, design, and planning.


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 material properties, sources, optimization of shapes.

C. The course is designed for master and Ph.D. students  in math, science, and engineering.


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


E. Text:
1. Optimization Theory with Applications  by Donald A. Pierre (Dover)
2. Instructor's Notes