MATLAB: Linear programming optimization for conditional

conditionallinear optimization

Is it possible to optimize this objective function using linear programming (linprog or intlinprog)? I have difficulties especially in defining I(i) and the max part (second term). Thanks!

minimize
    sum { I(i) * p(i)* (x(i) - x(i-1) + l(i) - g(i)) for i = 1, …, T } + max { pFix* (x(i) - x(i-1) + l(i) - g(i) for i = 1, …, T}
(I(i) = 0) if (x(i) - x(i-1) + l(i) - g(i) <= 0)
(I(i) = 1) if (x(i) - x(i-1) + l(i) - g(i) > 0)

Best Answer

If I understand you correctly, and if p(i) > 0, then instead of I(i) you can use

I(i) * p(i)* (x(i) - x(i-1) + l(i) - g(i)) = max[0,p(i)* (x(i) - x(i-1) + l(i) - g(i))]

If this is correct, then I believe that you cannot write your objective function as a linear function as required by intlinprog or linprog, because the objective is not linear in the variables x(i).

Alan Weiss

MATLAB mathematical toolbox documentation

Related Solutions

MATLAB: Constraint with decision variable

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.

MATLAB: Can I give a dependent constraint in Multiobjective Optimization using Genetic Algorithm

It is a linear constraint

 x(1)-x(3)<=0

Use the A,b input matrices to express it,

A=[1 0 -1 0 0 0];
b=0;

Best Answer

Related Solutions

MATLAB: Constraint with decision variable

MATLAB: Can I give a dependent constraint in Multiobjective Optimization using Genetic Algorithm

Related Question