Can the variables take on available minimum and maximum values automatically(like S(r,t) = 0 and V(r,t) = Vrmax) or it simply says infeasible.
If the solution lies there, the variables can take on these values. Bear in mind though, that you can never guarantee the solution will be found with perfect precision, nor that the constraints will be satisfied with perfect precision. It's an iterative approximation algorithm and, further, we live in a world of approximate digital arithmetic.
What will happen if S(r,t) results in a value less than zero or V(r,t) results in a value greater than Vrmax during the optimization at some stage. put in mind that Linprog is the function being used to solve the problem.
Nothing will happen. Many Optimization Toolbox algorithms search outside the feasible set, but try to satisfy the constraints asymptotically to within a tolerance governed by the TolCon option parameter. Linprog is the same, though you could select the simplex algorithm or active-set algorithm options, which try to restrict their search to the edges of the feasible set. Even then, of couse, you have precision limits on how exactly you can satisfy constraints.
