minimize nonlinear inequalities in matlab

In MATLAB, you can use the fmincon function to minimize non-linear inequalities. The general syntax of the fmincon function is as follows:

main.m
x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub)
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where

• fun is a handle to the objective function.
• x0 is the initial guess of the solution.
• A and b are matrices that define the non-linear inequality constraints A*x <= b.
• Aeq and beq are matrices that define the non-linear equality constraints Aeq*x = beq.
• lb and ub are the lower and upper bounds of the optimization variables.

Here's an example code that illustrates how to use fmincon to minimize a non-linear inequality:

main.m
% define the objective function
fun = @(x) 100*(x(2) - x(1)^2)^2 + (1 - x(1))^2;

% define the non-linear inequality constraints
A = [1 1];
b = 1;

% define the initial guess of the solution
x0 = [0 0];

% define the lower and upper bounds of the optimization variables
lb = [-inf -inf];
ub = [inf inf];

% call the fmincon function
[x, fval] = fmincon(fun, x0, A, b, [], [], lb, ub);
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In this example, the objective function is the Rosenbrock function, which has a non-linear inequality constraint x2 - x1 <= 1. The fmincon function is called with the objective function, the initial guess of the solution, the non-linear inequality constraint, and the lower and upper bounds of the optimization variables. The output x is the solution to the optimization problem, and fval is the value of the objective function at x.