fmincon to solve constrained optimization problem with a nonlinear constraint

3 次查看（过去 30 天）
BlkHoleSun
BlkHoleSun 2017-11-18
回答： BlkHoleSun 2017-12-3
I've got a challenging problem to solve using the fmincon function. I've attached the question and posted the code from the question I solved prior to this one to give you a better idea of what I'm doing. Thanks for your guidance...here's the previous code.
% Used for plotting as it contains both x and y
z2 = @(x,y) (x/(sqrt(x.^2 + y.^2))).*(besselj(1, 3.8316.*sqrt(x.^2 + y.^2)));
% Used for finding min at each function
z0 = @(x) (x(1)/(sqrt(x(1).^2 + x(2).^2))).*(besselj(1, 3.8316.*sqrt(x(1).^2 + x(2).^2)));
% Used to find max at each function due to multiplying by (-1)
z1 = @(x) (-1)*(x(1)/(sqrt(x(1).^2 + x(2).^2))).*(besselj(1, 3.8316.*sqrt(x(1).^2 + x(2).^2)));
% Defining initial conditions
a = [.5, -.5];
% Running min/max search using fminsearch function
[xi,fvali,exitflagi,outputi] = fminsearch(z0, a);
[xa,fvala,exitflaga,outputa] = fminsearch(z1, a);
% Running min/max search using fminunc function
[xi1,fvali1,exitflagi1,outputi1] = fminunc(z0, a);
[xa1,fvala1,exitflaga1,outputa1] = fminunc(z1, a);
% Plotting a max found from the search
hold on
ezmeshc(z2, [-1, 1, -1, 1]);
plot3(xa(1,1),xa(1,2), fvala , 'ob', 'MarkerSize', 12);
axis([-1 1 -1 1 -1 1]); % Expanded the axis to show marker
xlabel('x-axis');
ylabel('y-axis');
zlabel('z-axis');
legend('grid', 'rings', 'marker');
view(155, 9); % Adjusting starting orientation of plot
  1 个评论
BlkHoleSun
BlkHoleSun 2017-11-18
pressed on with a solution, but not confident I'm correct. All the parts are on the plot, but the max I found using the fmincon function doesn't seem right. below is the separate function code and problem code I've written for the problem:
Function Code:
function [c,ceq] = nonlcon(x)
%Non-linearinequalityconstraints:
c = (0.6)^2-(x(1)-0.4)^2 + (x(2)-0.4)^2;
ceq = [];
Problem Code:
% Used for plotting as it contains both x and y
z2 = @(x,y) (x/(sqrt(x.^2 + y.^2))).*(besselj(1, 3.8316.*sqrt(x.^2 + y.^2)));
% Used to find max at each function due to multiplying by (-1)
z1 = @(x) (-1)*(x(1)/(sqrt(x(1).^2 + x(2).^2))).*(besselj(1, 3.8316.*sqrt(x(1).^2 + x(2).^2)));
x0 = [0.5,-0.5];
[x,fval,exitflag,output] = fmincon(z1,x0,[],[],[],[],[],[],@nonlcon)
hold on
plot3(x(1,1),x(1,2), fval , 'ob', 'MarkerSize', 12);
ezmeshc(z2, [-1, 1, -1, 1]);
[x,y,z] = cylinder(0.6, 40);
mesh(x+0.4, y+0.4, 1.2*z-0.6, 'FaceAlpha', 0.8)
axis equal
view(-64, 14);
xlabel('x-axis');
ylabel('y-axis');
zlabel('z-axis');
legend('marker', 'grid', 'rings');

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

BlkHoleSun
BlkHoleSun 2017-12-3
%%Set up inline functions to be used for fmincon and plotting
clear all
% Used for plotting as it contains both x and y
z2 = @(x,y) (x/(sqrt(x^2 + y^2)))*(besselj(1, 3.8316.*sqrt(x^2 + y^2)));
% Used to find max due to multiplying by (-1)
z0 = @(x) ((x(1))/(sqrt((x(1))^2 + (x(2))^2)))*(besselj(1, 3.8316*(sqrt((x(1))^2 + (x(2))^2))));
z1 = @(x) -1*(x(1)/(sqrt((x(1)^2) + (x(2)^2))))*(besselj(1, (3.8316*(sqrt((x(1)^2)+(x(2)^2))))));
%%Using fmincon function with embedded nonlcon function to find max
a = [.5 ,-.5]; %Starting point from problem 3
[xa,fvala,exitflaga,outputa] = fmincon(z1,a,[],[],[],[],[],[],@nonlcon,[]);
maxit = outputa.iterations;
fprintf('The max number of iterations using fminunc is %2.0f. \n', maxit)
%%Creating plot with problem 3 function, constraint and max found
hold on
plot3(xa(1),xa(2), -fvala , 'ob', 'MarkerSize', 12);
ezmeshc(z2, [-1, 1, -1, 1]);
[x,y,z] = cylinder(0.6, 40);
mesh(x+0.4, y+0.4, 1.2*z-0.6, 'FaceAlpha', 0.8)
axis equal
view(-64, 14);
xlabel('x-axis'); ylabel('y-axis'); zlabel('z-axis');
title('z(x,y) vs max found vs cylinder constraint')
legend('marker', 'grid', 'rings');

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Global or Multiple Starting Point Search 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by