What algorithm can solve a linear minimization problem with given constraints?

[specone]

Hi all,

does anyone know what type of problem this would be classified as, and what kind of algorithm I could use to get a solution?

minimize:
P=60w₁+30w₂+10w₃+100w₄

subject to:
P ≥ 50
0 < w_i ≤ 1

thanks very much

 

[mathman]

What are you trying to minimize? Without this, the question is incomplete. Defining what you want to minimize with these conditions is called linear programing.

 

[AlephZero]

It looks like a Linear Programming problem. The most straightforward solution algorithm is the Simplex Method.

 

[HallsofIvy]

The fundamental result in "linear programming" is that a minimum or maximum of a linear function, in a convex polyhedron, must occur at a vertex of the polhedron. Your condition, $0< w_i\le 1$, says that the "feasible region" is a n-dimensional rectangle and it is easy to calculate its $2^n$ vertices. However, the condition S> 50, on the target function will have to be applied after determining values. Also the fact that the faces $0= w_i$ are NOT in the feasible region can be a problem.

 

[CellCoree]

I can tell you that this is a linear minimization problem. The objective is to minimize the cost function expressed as P=60w1+30w2+10w3+100w4 subject to the constraints that the total cost (P) must be greater than or equal to 50 and the weights (wi) must be between 0 and 1. This type of problem can be solved using linear programming algorithms such as the simplex method or the interior-point method. These algorithms will provide an optimal solution that minimizes the cost function while satisfying all the given constraints. I hope this helps!