clc; clear; close all;
% Initial guess for [x1, x2, x3] (adjust as needed)
x0 = [0.2,0.35,0.5];
% No linear constraints
A = []; b = [];
Aeq = []; beq = [];
% Lower and upper bounds (adjust based on the problem)
lb = [0,0,0];
ub = [pi/2,pi/2,pi/2];
% Optimization options
options = optimoptions('fmincon', 'Algorithm', 'sqp', 'Display', 'iter');
% Solve with fmincon
[x_opt, fval, exitflag] = fmincon(@objective, x0, A, b, Aeq, beq, lb, ub, @nonlinear_constraints, options);
% Display results
fprintf('Optimal Solution: x1 = %.4f, x2 = %.4f, x3 = %.4f\n', x_opt(1), x_opt(2), x_opt(3));
fprintf('Exit Flag: %d\n', exitflag);
%% Objective function (minimizing sum of squared errors)
function f = objective(x)
f = sum(x.^2); % Dummy function (since we only want to solve equations)
end
%% Nonlinear constraints (representing the trigonometric equations)
function [c, ceq] = nonlinear_constraints(x)
% Example nonlinear trigonometric equations:
ceq(1) = cos(x(1))+cos(x(2))+cos(x(3))-3*0.9; % First equation
ceq(2) = cos(5*x(1))+cos(5*x(2))+cos(5*x(3)); % Second equation
ceq(3) = cos(7*x(1))+cos(7*x(2))+cos(7*x(3)); % Third equation
c = [x(1)-x(2); x(2)-x(3)]; % No inequality constraints
end
