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Plot Functions

Plot an Optimization During Execution

You can plot various measures of progress during the execution of a solver. Set the PlotFcn name-value pair in optimoptions, and specify one or more plotting functions for the solver to call at each iteration. Pass a function handle or cell array of function handles.

There are a variety of predefined plot functions available. See the PlotFcn option description in the solver function reference page.

You can also use a custom-written plot function. Write a function file using the same structure as an output function. For more information on this structure, see Output Function and Plot Function Syntax.

Use a Plot Function

This example shows how to use plot functions to view the progress of the fmincon 'interior-point' algorithm. The problem is taken from Constrained Nonlinear Problem Using Optimize Live Editor Task or Solver.

Write the nonlinear objective and constraint functions, including their gradients. The objective function is Rosenbrock's function.

type rosenbrockwithgrad
function [f,g] = rosenbrockwithgrad(x)
% Calculate objective f
f = 100*(x(2) - x(1)^2)^2 + (1-x(1))^2;

if nargout > 1 % gradient required
    g = [-400*(x(2)-x(1)^2)*x(1)-2*(1-x(1));

Save this file as rosenbrockwithgrad.m.

The constraint function is that the solution satisfies norm(x)^2 <= 1.

type unitdisk2
function [c,ceq,gc,gceq] = unitdisk2(x)
c = x(1)^2 + x(2)^2 - 1;
ceq = [ ];

if nargout > 2
    gc = [2*x(1);2*x(2)];
    gceq = [];

Save this file as unitdisk2.m.

Create options for the solver that include calling three plot functions.

options = optimoptions(@fmincon,'Algorithm','interior-point',...

Create the initial point x0 = [0,0], and set the remaining inputs to empty ([]).

x0 = [0,0];
A = [];
b = [];
Aeq = [];
beq = [];
lb = [];
ub = [];

Call fmincon, including the options.

fun = @rosenbrockwithgrad;
nonlcon = @unitdisk2;
x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)

Figure Optimization Plot Function contains 3 axes objects. Axes object 1 with title Current Point, xlabel Number of variables: 2, ylabel Current point contains an object of type bar. axes object 2 with title Current Function Value: 0.0456748, xlabel Iteration, ylabel Function value contains a line object which displays its values using only markers. axes object 3 with title First-order Optimality: 2.16246e-08, xlabel Iteration, ylabel First-order optimality contains a line object which displays its values using only markers.

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
x = 1×2

    0.7864    0.6177

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