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)); 200*(x(2)-x(1)^2)]; end
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 = []; end
Save this file as unitdisk2.m
.
Create options for the solver that include calling three plot functions.
options = optimoptions(@fmincon,'Algorithm','interior-point',... 'SpecifyObjectiveGradient',true,'SpecifyConstraintGradient',true,... 'PlotFcn',{@optimplotx,@optimplotfval,@optimplotfirstorderopt});
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)
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