# Solving a non-linear program using Python

New to optimization, trying to understand the characteristics of a problem I am in the process of modelling, and looking to solve in Python. Given is a decision variable k,the sum of N other decision variables c, and two constants, a and T. Both a and T are positive numbers.

I want to maximize k subject to (a + c) * k <= T.

What kind of problem is this? I can see that the chosen values for c maximizes k. In addition, they are multiplied together in a constraint, which followingly does not look linear, i.e. this is not a Linear Program.

At the time of writing, I am only familiar with Google OR-Tools as a means to solve optimization problems, and if this problem is either non-linear or quadratic, I might need something else to solve it.

Any clues on what I am looking for here?

• It looks like a quadratic problem since you have a sum of products of two variables. Depending on the signs of the various constants it will be convex or not ie. relatively easy or relatively hard. You would have to provide more details. Commented Mar 14 at 14:00
• Yes, all constants are positive real numbers. Updated post. Commented Mar 15 at 8:13