MATLAB: Constraint with decision variable

constraintoptimization

How can I write a constraint for optimization which includes the decision variable (x)? The constraint is:
max (0, x(i-1) - P) <= x(i) <= min (C, x(i-1) + D)

Best Answer

You should use a couple of different kinds of constraints. But you are only constraining variable #i, so we have to initialize the constraints so the other variables are not affected
Nx = length(x);
%no equality constraints
Aeq = [];
beq = [];
%the constraint has to be for some _specific_ i
i = 13;
%now to construct x(i-1) - P <= x(i) and x(i) <= x(i-1) + D
A = zeros(2, Nx);
b = zeros(2, 1);
A(1, i-1) = 1; A(1, i) = -1; b(1) = P;   % (1)  * x(i-1) + (-1) * x(i) <= (P)
A(2, i-1) = -1; A(2, i) = 1; b(2) = D;   % (-1) * x(i-1) + (1)  * x(i) <= (D)
%lower bounds are -inf, upper bounds are +inf for all variables except #i
lb = -inf * ones(1, Nx);
ub = inf * ones(1, Nx);
%but for variable #i, the value cannot be less than 0 or more than C
lb(i) = 0;
ub(i) = C;
fmincon(@objective, x0, A, b, Aeq, beq, lb, ub)
Your constraints cannot be generalized to all of the variables because there is no x(0) to constrain x(1) against.
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