## How to Use All Types of Constraints

This section contains an example of a nonlinear minimization problem with all possible types of constraints. The objective function is in the local function `myobj(x)`. The nonlinear constraints are in the local function `myconstr(x)`. This example does not use gradients.

```function [x fval exitflag] = fullexample x0 = [1; 4; 5; 2; 5]; lb = [-Inf; -Inf; 0; -Inf; 1]; ub = [ Inf; Inf; 20; Inf; Inf]; Aeq = [1 -0.3 0 0 0]; beq = 0; A = [0 0 0 -1 0.1 0 0 0 1 -0.5 0 0 -1 0 0.9]; b = [0; 0; 0]; opts = optimoptions(@fmincon,'Algorithm','sqp'); [x,fval,exitflag]=fmincon(@myobj,x0,A,b,Aeq,beq,lb,ub,... @myconstr,opts) %--------------------------------------------------------- function f = myobj(x) f = 6*x(2)*x(5) + 7*x(1)*x(3) + 3*x(2)^2; %--------------------------------------------------------- function [c, ceq] = myconstr(x) c = [x(1) - 0.2*x(2)*x(5) - 71 0.9*x(3) - x(4)^2 - 67]; ceq = 3*x(2)^2*x(5) + 3*x(1)^2*x(3) - 20.875;```
Calling `fullexample` produces the following display in the Command Window:
```[x fval exitflag] = fullexample; 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 = 0.6114 2.0380 1.3948 0.1572 1.5498 fval = 37.3806 exitflag = 1```

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