# Dynamic bounds in an optimizer

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Spyros Polychronopoulos on 18 Jun 2020
Answered: Alan Weiss on 19 Jun 2020
I would like to have relationship constraints between variables an optimizer is trying. For example: If variable x(1) is greater than 10 then 8<= x(2) <= 12.
O = @(x) x(1)+x(2)+x(3);
IN= [10 10 10]; % Initial Values
LB=[5 5 5]; % Low Bound
UB=[15 15 15]; % Upper Bound
[set_matrix,best_cost]=simulannealbnd(O,IN,LB,UB); % Simulated Annealing
% if x(1)>10 then x(2) has to take values between 8 and 12

Alan Weiss on 19 Jun 2020
You are describing a nonlinear constraint. This is a type of constraint that simulannealbnd cannot handle.
In fact, your constraint is not differentiable. This can be a problem for solvers. However, if your underlying variables are integer-valued, then you can use some techniques from integer linear programming to create the constraint. See Optimal Dispatch of Power Generators for an example.
Solvers that can handle nonlinear constraints include fmincon, patternsearch, ga, and the recent version of surrogateopt. Solvers that handle integer variables include intlinprog, ga, and surrogateopt.
Alan Weiss
MATLAB mathematical toolbox documentation