Linear Programming with Constraints

1
votes

Is there any known algorithm to find a maximum when there is a constraint on the optimizing function. i.e. I am interested to find the maximum of

cTx

under the constraint

Ax <= b

however I also request that

cTx <= α

It looks similar to the simplex algorithm but I have an additional constraint on the maximizing cost.

1
linear-programming
You might have more luck at the Math sister site: math.stackexchange.com FWIW you'd likely need something that solves non-linear, possibly non-convex programs. I.E, this is no longer linear programming. - AndyG
Introduce a new variable z and a constraint z=cTranspose*x. Append your desired constraint z <= alpha to the problem and replace the original objective with max z. Any half-resonable linear programming solver / modeling environment will support such changes to your LP problem. It is still solvable with the simplex method. - Ali

1 Answers

0
votes

The simplex algorithm can deal with any linear constraints and linear objective function. There is nothing special at all if some linear constraint constains the objective function. Any LP solver can do the trick! It might be handful though to add a new decision variable, equal to the objective function.