Linear Programming with Constraints

Question

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

c^Tx

under the constraint

Ax <= b

however I also request that

c^Tx <= α

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

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
– AndyG, Commented Feb 17, 2014 at 21:28
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
– Ali, Commented Feb 17, 2014 at 22:13

IPV3001 · Accepted Answer · 2014-02-19 09:35:58Z

0

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.

answered Feb 19, 2014 at 9:35

IPV3001

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