Problem finding maximum of a nonlinear problem

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Jaime De La Mota Sanchis 2022-7-15

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https://ww2.mathworks.cn/matlabcentral/answers/1760670-problem-finding-maximum-of-a-nonlinear-problem

编辑： Torsten 2022-7-15

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I have the following problem.

Minimize

subject to

and

I am trying to use fmincon to find this point.

My attempt as solutuion is as follows:

close all
clear
clc
fun = @(x) x(1)+x(2)+x(3); %minimize
lb = [];
ub=[];
x0 = [1 1 1];
A = [];
b=[];
Aeq=[];
beq=[];
x = fmincon(fun,x0,A,b, Aeq, beq, lb, ub, @constraints)
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 = 1×3
   -1.4142    0.2929   -0.7071
function [c,ceq] = constraints(x)
    c=[0 0];
    c(1) = (x(2)-1).^2+x(3).^2-1; % <=0
    c(2) = x(1).^2+(x(2)-1).^2+x(3).^2-3;
    ceq = [];
end