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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 Solve a Constrained Nonlinear Problem, Solver-Based.

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 contains an object of type bar. Axes object 2 with title Current Function Value: 0.0456748 contains an object of type line. Axes object 3 with title First-order Optimality: 2.16246e-08 contains an object of type line.

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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