I would like to use ALGENCAN to optimize many problems of the following type
minimize 1/2 * X' A X - c X
subject to b<= X <= 1
Sum_i x_i = 1
Also, the matrix A is diagonal but could have negative entries. So I have a quadratic programming problem with only one linear equality constraint and upper/lower bounds. In my case X is large. (could have at most 100k entries)
I had two questions
1. I don't know much about optimization so I was reading around for a simple polynomial time algorithm to solve my problem exactly. I found a O(n) time algorithm but the restriction is that matrix A should have entries > 0. Does anyone know of an algorithm for the general case where the diagonal elements in A can be any real number.
2. If there isn't a solution to 1, I'd like to use ALGENACN for my problem. I'm trying it out right now and after reading some of the messages in the group, I'm using the following options in my algencan.dat file
I've compiled ALGENCAN with ma57 as well. Should I be using other options ? I have to otimize thousands of optimizations of the aforementioned type so running time is important here.I kept the tolerances high because I didn't want a very accurate solution at the expense of time. Is that the right way to go ? Any suggestions are welcome.