Nonlinear Equations and Optimization M-563

Spring 1997. Three credit hours

Instructor:


8:50 - 9:40 MWF, in JWB 208.


TEXT: `Practical Optimization' Chapters 1, 2, 3, 4, 5, 6.


Course content

The main problem of engineering is: how to increase the efficiency of a process, of a construction, etc. To achieve this goal the designer can choose several parameters (controls), assuming that certain constrains are satisfied. Mathematical formulation of the optimization problem deals with those three objects: the goal function, the controls, the constrains. Methods to effective search for an optimal values of controls are formed the Optimization Theory. The modern branches of Optimization Theory include Optimal Control, Structural Optimization, etc. We discuss and compare methods and algorithms of optimization. The most suitable method depends on the type of the problem considered: of the number of controls, smoothness of constrains/goal function, etc. We try different methods in different situations to experience in optimization techniques.

The ten weeks of classes will be roughly divided as following:

  • 1. Introduction, 1 week (chapter 1, 2.1, 2.3)
  • 2. Optimality conditions (unconstrained and constrained optimization), 1 week (chapter 3)
  • 3. Unconstrained Methods, 3 weeks (chapter 4 )
  • 4. Linear constraints, 2 weeks (chapter 5)
  • 5. Non-linear constraints, 3 weeks (chapter 6)
  • A research project `Optimization of a mechanical element' will be suggested. Two report talks are to be given by each group of students and a final report is to be submitted.


    Prerequisites

    M 251, M 252, M 353 or equivalents.

    Grading policy:

    Homework assignments:

    second assignment,


    Notes and comments to lectures: