Enormous matrix (C++) (Visual Studio 2015) (QuadProg library)

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I'm trying to use QuadProg++ library. The problem is that my CI variable is enormous. Up to 40,000 * 20,000. With this size, it will take too much memory (12GB at least.....). I have 2 questions: 1.- There are any way to give to the "solve_quadprog" function different data types than double for the matrix? I tried with short, but it didn't allowed me. 2.- Anyone knows how to solve this size problem? this CI variable is very simple in fact, only a diagonal with all 1's, and other diagonal with all -1 (all other values are 0)

If is possible to solve these problems using another library (with solves the quadratic programming problem) is not a problem too. Any solution will be appreciated Thanks in advance

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