mathematical-optimization

I have written the following function which finds all divisors of a given natural number and returns them as a list: def FindAllDivisors(x): divList = [] y = 1 while y <= math.sqrt(x): if x % y == 0: divList.append(y) divList.append(int(x / y)) y += 1 return divList It works really well with the exception that it's really slow when the input is say an 18-digit number. Do you have any suggestions for how I can speed it up? Update : I have the following method to check for primality based on Fermat's Little Theorem: def CheckIfProbablyPrime(x): return (2 << x - 2) % x == 1 This method is really

I have an optimization problem that has in the objective function 2 multiplied variables, making the model quadratic. I am currently using zimpl, to parse the model, and glpk to solve it. As they don't support quadratic programming, I would need to convert this to an MILP. . The first variable is real, in range [0, 1], the second one is real, from range 0 to inf. This one could without a problem be integer. The critical part in the objective function looks like this: max ... + var1 * var2 + ... I had similar problems in the constraints, but they were easily solvable. How could I solve this

I have a set of integers M and a target sum k. I want to find the subset of M that when added together is the closest to k without going over. For example: M = {1, 3, 5, 5, 14} k = 12 answer = {1, 5, 5} because 1 + 5 + 5 = 11 and there is no way to make 12. I have the additional constraint that the subset can contain at most 4 elements. In my application, the size of |M| can be large (on the order of thousands of elements). If it is not possible to find the optimal answer in a reasonable time, I am interested in solutions that at least give a "good" answer. Right now I am solving this problem

I would like students to solve a quadratic program in an assignment without them having to install extra software like cvxopt etc. Is there a python implementation available that only depends on NumPy/SciPy? I ran across a good solution and wanted to get it out there. There is a python implementation of LOQO in the ELEFANT machine learning toolkit out of NICTA ( http://elefant.forge.nicta.com.au as of this posting). Have a look at optimization.intpointsolver. This was coded by Alex Smola, and I've used a C-version of the same code with great success. I'm not very familiar with quadratic

Just looking for a bit of direction, I realise that the example given is possible to solve using brute force iteration, but I am looking for a more elegant (ie. mathematical?) solution which could potentially solve significantly larger examples (say 20x20 or 30x30). It is entirely possible that this cannot be done, and I have had very little success in coming up with an approach which does not rely on brute force... I have a matrix (call it A) which is nxn. I wish to select a subset (call it B) of points from matrix A. The subset will consist of n elements, where one and only one element is

Is there any optimization library in C#? I have to optimize a complicated equation in excel, for this equation there are a few coefficients. And I have to optimize them according to a fitness function that I define. So I wonder whether there is such a library that does what I need? ShuggyCoUk Here are a few free and open source c# implementrions Nelder Mead Simplex implementation [ Alternate Link ] Numerical provides a variety of algorithms including: Chromosome Manager Genetic Optimizer Hill Climbing Optimizer Maximizing Point Maximizing PointFactoy Maximizing Vector Minimizing Point