I am wondering if it is possible to optimize for higher average values with an MIP solver like Gurobi Specifically I have the following problem that I am interested in solving subject to some linear constraints. One way of solving it would be to solving it in different steps by assuming a threshold for which we want the objective to be higher than that. i.e but I am wondering if there is any easier way of solving it (perhaps Gurobi can solve it directly with some tricks?) Thanks asked 25 Nov '13, 17:52 Igor Pangal fbahr ♦ 
You can linearize the fractional 01 program, thereby turning it into a standard MIP. For example, use the approach proposed by Wu: Introduce new variables \( y=\frac{1}{\sum_{i} x_i}\) and \( z_i = y x_i\). Make this your formulation (after including binary restrictions on x variables and add all your other constraints). maximize \( \sum_{i} w_i z_i \) \(z_i \le U x_i \) \(z_i \ge L x_i \) \(z_i \le y  L (1x_i) \) \(z_i \ge y  U (1x_i) \) \( \sum_{i} z_i =1\) \( L \le y \le U\) \( z_i \ge 0\) where \( L=\frac{1}{n}\),\(U =1\), and n is the number of 01 variables. The new, weirdlooking constraints are introduced to linearize the quadratic terms \( y x_i\). answered 25 Nov '13, 20:42 Austin Buchanan This is right, my previous answer was wrong.
(25 Nov '13, 20:50)
Iain Dunning

Are there integer variables present? If so, are they binary?
yes x_i is a binary variable and w_i is just a constant number for each x_i