Difference between revisions of "Non-linear programming"

From Optimization for Chemical Engineering: 4G3
Jump to navigation Jump to search
 
(3 intermediate revisions by the same user not shown)
Line 60: Line 60:
! Topic
! Topic
! Slides/handouts for class
! Slides/handouts for class
! Video file
! References and Notes
! References and Notes
|-
|-
Line 70: Line 69:
| align="left" colspan="1"|
| align="left" colspan="1"|
[https://docs.google.com/document/d/1NozRUYfdIw2RLnU0DExOzF-RH-mx5VbjgQU35zxKLCU  Handout from class]
[https://docs.google.com/document/d/1NozRUYfdIw2RLnU0DExOzF-RH-mx5VbjgQU35zxKLCU  Handout from class]
| [http://learnche.mcmaster.ca/media/2015-4G3-Class-05A.mp4  Video]
|align="left" colspan="1"|
|align="left" colspan="1"|
|-
|-
Line 81: Line 79:
| align="left" colspan="1"|
| align="left" colspan="1"|
[https://docs.google.com/document/d/10oe_laMhtPl5roJGa3C44YlsSvdbHvUAjt6uRMf9q4k  Handout from class]
[https://docs.google.com/document/d/10oe_laMhtPl5roJGa3C44YlsSvdbHvUAjt6uRMf9q4k  Handout from class]
| [http://learnche.mcmaster.ca/media/2015-4G3-Class-06A.mp4  Video]
|align="left" colspan="1"|
|align="left" colspan="1"|
|-
|-
Line 92: Line 89:
| align="left" colspan="1"|
| align="left" colspan="1"|
[https://docs.google.com/document/d/1h9qLQbzeeqtQjf3l9Rmwx-5UKZF-ac2ZqMioupda8cs  Handout from class]
[https://docs.google.com/document/d/1h9qLQbzeeqtQjf3l9Rmwx-5UKZF-ac2ZqMioupda8cs  Handout from class]
| [http://learnche.mcmaster.ca/media/2015-4G3-Class-06B.mp4  Video]
|align="left" colspan="1"|
|align="left" colspan="1"|
|-
|-
Line 108: Line 104:
| align="left" colspan="1"|
| align="left" colspan="1"|
[https://docs.google.com/document/d/1vg7ffZUjSSmh1pL1EgeCGJtQnCSC652UWaBanfmqXr0 Handout from class]
[https://docs.google.com/document/d/1vg7ffZUjSSmh1pL1EgeCGJtQnCSC652UWaBanfmqXr0 Handout from class]
| [http://learnche.mcmaster.ca/media/2015-4G3-Class-08A.mp4  Video]
|align="left" colspan="1"|
|align="left" colspan="1"|
|-
|-
Line 119: Line 114:
| align="left" colspan="1"|
| align="left" colspan="1"|
[https://docs.google.com/document/d/1tISkFj7nYa3RV7G8LF4S_nD7dMzb7_ATwY0z4gslDT0 Handout from class]
[https://docs.google.com/document/d/1tISkFj7nYa3RV7G8LF4S_nD7dMzb7_ATwY0z4gslDT0 Handout from class]
| [http://learnche.mcmaster.ca/media/2015-4G3-Class-08B.mp4 Video]
|align="left" colspan="1"|
|align="left" colspan="1"|
Code used in class (see below)
Code used in class (see below)
Line 130: Line 124:
| align="left" colspan="1"|
| align="left" colspan="1"|
[https://docs.google.com/document/d/1tHekhHdPWEPhPm_lGVP5cws_2-NsTw_6JpVhhLSlgmo Handout from class]  
[https://docs.google.com/document/d/1tHekhHdPWEPhPm_lGVP5cws_2-NsTw_6JpVhhLSlgmo Handout from class]  
|[http://learnche.mcmaster.ca/media/2015-4G3-Class-09A.mp4 Video]
|align="left" colspan="1"|
|align="left" colspan="1"|
|-
|-
Line 139: Line 132:
| align="left" colspan="1"|
| align="left" colspan="1"|
[[Media:Guest-lecture-4G3-2015.pdf |Handout from class]]
[[Media:Guest-lecture-4G3-2015.pdf |Handout from class]]
|http://learnche.mcmaster.ca/media/2015-4G3-Class-09B.mp4 Video]
|align="left" colspan="1"|
|align="left" colspan="1"|
|-
|-
Line 149: Line 141:
| align="left" colspan="1"|
| align="left" colspan="1"|
[https://docs.google.com/document/d/1tHekhHdPWEPhPm_lGVP5cws_2-NsTw_6JpVhhLSlgmo Handout from class]  (continued with handout 09A)
[https://docs.google.com/document/d/1tHekhHdPWEPhPm_lGVP5cws_2-NsTw_6JpVhhLSlgmo Handout from class]  (continued with handout 09A)
| [http://learnche.mcmaster.ca/media/2015-4G3-Class-10A.mp4 Video]
|align="left" colspan="1"|
|align="left" colspan="1"|
|-
|-
Line 159: Line 150:
| align="left" colspan="1"|
| align="left" colspan="1"|
[https://docs.google.com/document/d/14F-MRq34UNR52Wg2JL9MalYfVZIOHjYCTkRa9tgGQ7g/edit?usp=sharing Handout from class]
[https://docs.google.com/document/d/14F-MRq34UNR52Wg2JL9MalYfVZIOHjYCTkRa9tgGQ7g/edit?usp=sharing Handout from class]
| [http://learnche.mcmaster.ca/media/2015-4G3-Class-10BA.mp4 Video]
|align="left" colspan="1"|
|align="left" colspan="1"|
|-
|-
Line 169: Line 159:
| align="left" colspan="1"|
| align="left" colspan="1"|
[https://docs.google.com/document/d/1QdpFX1wgiCfNXgEJz9r6j85k4vXXfwbDPo9weKuCFR0/edit?usp=sharing Handout from class]
[https://docs.google.com/document/d/1QdpFX1wgiCfNXgEJz9r6j85k4vXXfwbDPo9weKuCFR0/edit?usp=sharing Handout from class]
|  [http://learnche.mcmaster.ca/media/2015-4G3-Class-11A.mp4 Video]
|align="left" colspan="1"|
|align="left" colspan="1"|
|}
|}

Latest revision as of 11:57, 12 August 2018

Class date(s): 04 February 2015










Resources

Scroll down, if necessary, to see the resources.

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

Handout from class

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

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

Handout from class

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

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

Code used in class (see below)

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

Handout from class

11 March 09B

Guest lecture

Handout from class

16 March 10A
  • Convexity, concavity
  • Guarantees on when problems are globally optimal

Handout from class (continued with handout 09A)

18 March 10B
  • Lagrange multiplier method for constrained optimization
  • Interpretation of the Lagrange multiplier constraints

Handout from class

23 March 11A
  • The Nelder-Mead method (several of you are using it in your projects)
  • Practice with using the Nelder Mead method. Optimize this system: http://yint.org/nm

Handout from class



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];