linear-programming

I'm trying to set up a linear program in which the objective function adds extra weight to the max out of the decision variables multiplied by their respective coefficients. With this in mind, is there a way to use min or max operators within the objective function of a linear program? Example: Minimize (c1 * x1) + (c2 * x2) + (c3 * x3) + (c4 * max(c1*x1, c2*x2, c3*x3)) subject to #some arbitrary integer constraints: x1 >= ... x1 + 2*x2 <= ... x3 >= ... x1 + x3 == ... Note that (c4 * max(c1*x1, c2*x2, c3*x3)) is the "extra weight" term that I'm concerned about. We let c4 denote the "extra

Does anyone know of such a library that performs mathematical optimization (linear programming, convex optimization, or more general types of problems)? I'm looking for something like MATLAB, but with the ability to handle larger problems. Do I have to write my own implementations, or buy one of those commercial products (CPLEX and the like)? A good answer is dependent on what you mean by "convex" and "more general" If you are trying to solve large or challenging linear or convex-quadratic optimization problems (especially with a discrete component to them), then it's hard to beat the main

I am using CPLEX for solving huge optimization models (more than 100k variables) now I'd like to see if I can find an open source alternative, I solve mixed integer problems (MILP) and CPLEX works great but it is very expensive if we want to scale so I really need to find an alternative or start writing our own ad-hoc optimization library (which will be painful) Any suggestion/insight would be much appreciated I personally found GLPK better (i.e. faster) than LP_SOLVE. It supports various file formats, and a further advantage is its library interface, which allows smooth integration with your