Difference between revisions of "Non-linear programming"

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* Constrained nonlinear optimization introduction
* Model formulation (convert a problem to mathematics)
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[[Media:Guest-lecture-4G3-2015.pdf Handout from class]]
[[Media:Guest-lecture-4G3-2015.pdf |Handout from class]]
|[https://www.dropbox.com/s/e2ietuldg34rce6/2015-4G3-Class-09B.mp4?dl=1 Video]  
|[https://www.dropbox.com/s/e2ietuldg34rce6/2015-4G3-Class-09B.mp4?dl=1 Video]  
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|align="left" colspan="1"|

Revision as of 21:32, 13 March 2015

Class date(s): 04 February 2015
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Resources

Scroll down, if necessary, to see the resources.

Date Class number Topic Slides/handouts for class Video file References and Notes
04 February 05A
  • Why consider unconstrained, single-variable problems
  • Newton's method review to solve these problems

Handout from class

Video
09 February 06A
  • Newton's method reviewed again for unconstrained, single-variable problems
  • Using finite differences instead in Newton's method
  • Multivariate unconstrained optimization

Handout from class

Video
11 February 06B
  • Unconstrained single-variable optimization using gradient search
  • Unconstrained multivariate optimization using gradient search
  • Understanding the line search problem

Handout from class

Video
16 to 27 February 07

Reading week break and midterm

02 March 08A
  • Unconstrained optimization in two variables review
  • Contrasting it back to the single variable case
  • Extending to the multidimensional Newton's method

Handout from class

Video
04 March 08B
  • Examples on the multidimensional Newton's method
  • Quasi Newton method in multiple dimensions
  • Positive and negative definiteness of the Hessian

Handout from class

Video

Code used in class (see below)

09 March 09A
  • Constrained nonlinear optimization introduction
  • Model formulation (convert a problem to mathematics)

Handout from class

Video
11 March 09B

Handout from class

Video


Taking full Newton's steps to solve the class example

clear all;
close all;
clc;
[X1,X2] = meshgrid(-0.5:0.1:6, 0:0.01:9);
Z = func(X1,X2);
contour(X1, X2, Z)
hold on
grid on

x = [1,3]';
plot(x(1), x(2), 'o')
text(x(1)+0.2, x(2), '0')

for k = 1:10
   slope = -first_deriv(x)
   step = hessian(x)\slope;   % Solves the Ax=b problem, as x = A\b
   x = x + step;
   plot(x(1), x(2), '*')
   text(x(1)+0.1, x(2), num2str(k))
end

func.m

function y = func(x1,x2)
  y = 4.*x1.*x2 - 5.*(x1-2).^4 - 3.*(x2-5).^4;

first_deriv.m

function y = first_deriv(x)
  y = [4*x(2) - 20*(x(1)-2)^3; 
       4*x(1) - 12*(x(2)-5)^3];

hessian.m

function y = hessian(x)
  y = [-60*(x(1)-2)^2, 4; 
        4, -36*(x(2)-5)^2];