We consider the following problem min f(x) = x>Qx + c>x + d s.t. Ax = b (1) x = 0 with Q ?Rn×n, c ?Rn, d ?R, A ?Rm×n and b ?Rm. When the size of the problem is large, very often it is more convenient to take advantage of smart or ad-hoc strategies to tackle the problem. Column generation, described for example in [3], represents one of the most important ways to deal with large-scale problems. In thi work we present a column generation algorithm called Simplicial Decomposition. We develop new techniques in order to make it more efficient and we compare our algorithm against the state-of-the-art software CPLEX. We present our algorithm and show our results, obtained on portfolio optimization problems and on general convex quadratic problems.
Simplicial decomposition for large-scale quadratic convex programming
Rinaldi F.;
2020
Abstract
We consider the following problem min f(x) = x>Qx + c>x + d s.t. Ax = b (1) x = 0 with Q ?Rn×n, c ?Rn, d ?R, A ?Rm×n and b ?Rm. When the size of the problem is large, very often it is more convenient to take advantage of smart or ad-hoc strategies to tackle the problem. Column generation, described for example in [3], represents one of the most important ways to deal with large-scale problems. In thi work we present a column generation algorithm called Simplicial Decomposition. We develop new techniques in order to make it more efficient and we compare our algorithm against the state-of-the-art software CPLEX. We present our algorithm and show our results, obtained on portfolio optimization problems and on general convex quadratic problems.Pubblicazioni consigliate
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