# Notes - Tutorial for the Optimization Toolbox...

This preview shows pages 1–4. Sign up to view the full content.

Tutorial for the Optimization Toolbox file:///C:/Program%20Files/MATLAB/R2007a%20Student/toolbox/opti... 1 of 11 8/21/2008 5:03 PM Run in the Command Window Tutorial for the Optimization Toolbox This is a demonstration for the medium-scale algorithms in the Optimization Toolbox. It closely follows the Tutorial section of the users' guide. All the principles outlined in this demonstration apply to the other nonlinear solvers: FGOALATTAIN, FMINIMAX, LSQNONLIN, FSOLVE. The routines differ from the Tutorial Section examples in the User's Guide only in that some objectives are anonymous functions instead of M-file functions. Contents Unconstrained Optimization Example Constrained Optimization Example: Inequalities Constrained Optimization Example: Inequalities and Bounds Constrained Optimization Example: User-Supplied Gradients Constrained Optimization Example: Equality Constraints Changing the Default Termination Tolerances Unconstrained Optimization Example Consider initially the problem of finding a minimum of the function: 2 2 f(x) = exp(x(1)) . (4x(1) + 2x(2) + 4x(1).x(2) + 2x(2) + 1) Define the objective to be minimized as an anonymous function: fun = @(x) exp(x(1)) * (4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + 1) fun = @(x)exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1) Take a guess at the solution: x0 = [-1; 1]; Set optimization options: turn off the large-scale algorithms (the default): options = optimset( 'LargeScale' , 'off' ); Call the unconstrained minimization function: [x, fval, exitflag, output] = fminunc(fun, x0, options); Optimization terminated: relative infinity-norm of gradient less than options.TolFun. The optimizer has found a solution at: x Open tutdemo.m in the Editor

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Tutorial for the Optimization Toolbox file:///C:/Program%20Files/MATLAB/R2007a%20Student/toolbox/opti... 2 of 11 8/21/2008 5:03 PM x = 0.5000 -1.0000 The function value at the solution is: fval fval = 3.6609e-015 The total number of function evaluations was: output.funcCount ans = 66 Constrained Optimization Example: Inequalities Consider the above problem with two additional constraints: 2 2 minimize f(x) = exp(x(1)) . (4x(1) + 2x(2) + 4x(1).x(2) + 2x(2) + 1) subject to 1.5 + x(1).x(2) - x(1) - x(2) <= 0 - x(1).x(2) <= 10 The objective function this time is contained in an M-file, objfun.m: type objfun function f = objfun(x) % Objective function % Copyright 1990-2004 The MathWorks, Inc. % \$Revision: 1.1.6.1 \$ \$Date: 2006/11/11 22:48:52 \$ f = exp(x(1)) * (4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + 1); The constraints are also defined in an M-file, confun.m: type confun function [c, ceq] = confun(x) % Nonlinear inequality constraints: % Copyright 1990-2004 The MathWorks, Inc. % \$Revision: 1.1.6.1 \$ \$Date: 2006/11/11 22:48:27 \$ c = [1.5 + x(1)*x(2) - x(1) - x(2);
Tutorial for the Optimization Toolbox file:///C:/Program%20Files/MATLAB/R2007a%20Student/toolbox/opti... 3 of 11 8/21/2008 5:03 PM -x(1)*x(2) - 10]; % No nonlinear equality constraints: ceq = []; Take a guess at the solution: x0 = [-1 1]; Set optimization options: turn off the large-scale algorithms (the default) and turn on the display of results at each iteration: options = optimset( 'LargeScale' , 'off' , 'Display' , 'iter' ); Call the optimization algorithm. We have no linear equalities or inequalities or bounds, so we pass [] for

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern