Continuous Optimization Outline for the New:
Computational Mathematics for Industry and Commerce Program
2001

URL: http://orion.math.uwaterloo.ca:80/~hwolkowi/henry/teaching/w01/367.w01/367miscfiles/outlinecompmath.html
Prerequisites: Linear Programming and Multivariate Calculus
This is a hands on course. Assignments will be a mixture of theory and numerical problems. We use various optimization packages, e.g:
MATLAB's optimization toolbox;
NEOS, and the Optimization Technology Center;
NAG, The Numerical Algorithms Group (available within MATLAB);
Decision Tree for Optimization Software;
NETLIB.
Part 1

Part 1, C&O 367



  1. Classifications of Problems
  2. Optimality Conditions
  3. Numerical Examples and Programming Notes
Part 2, C&O 367

Part 2, C&O 367



  1. Introduction to: Methods for Unconstrained Continuous Multivariate Problems
  2. Line Search and Trust Region Steps
  3. Convergence Criteria and Rates
Part 3, C&O 367

Part 3, C&O 367



  1. Gradient Methods for Unconstrained Minimization
  2. Steepest Descent
  3. Preconditioning, Rates of Convergence, Motivation for Newton's Method
  4. Numerical tests to illustrate convergence rates
Part 4, C&O 367

Part 4, C&O 367



  1. Newton's Method for Nonlinear Equations and Unconstrained Minimization (with variations: quasi-Newton, inexact Newton)
  2. After covering Newton's method, and some convergence theory for it, we provide experiments to allow students to experiment with the zones of attractions of critical points both with Matlab etc. and with the theoretical tools from the lectures.
Part 5, C&O 367

Part 5, C&O 367



  1. Convex Sets and Convex Functions
  2. Hyperplane separation/support Theorems.
Part 6, C&O 367

Part 6, C&O 367



  1. Introduction to Constrained Optimization
  2. Optimality Conditions (KKT) and Lagrangian Duality (with sensitivity analysis)
  3. Convex Programming (conditioning, ill-posedness)
Part 7, C&O 367

Part 7, C&O 367



  1. Introduction to Methods for Constrained Continuous Multivariate Problems
  2. Sequential Quadratic Programming methods as an extension of Trust Region Methods for Unconstrained Optimization (based on a quadratic model)
  3. Interior-Point Methods (Penalty and Barrier Methods)

Mail to: hwolkowicz@.uwaterloo.ca
(C) Copyright Henry Wolkowicz, 1991.
, by Henry Wolkowicz