I am trying to solve a QP problem.
Does anybody know the differences between the interior-point-convex algorithm of quadprog and the barrier method of Gurobi in terms which kind of matrices can the solvers handle the best? Sparse matrices or dense matrices? And what kind of problems: large problems or small problems? Furthermore, which solver needs more iterations (with less expensive cost per iteration) and which solver needs fewer iterations, but expensive cost/time per iteration.
From results, I think Gurobi gives more iterations and quadprog less, but I do not know why?
And what are the differences with GPAD by means of what is described above?
Dear Soufyan,
The interior-point-convex of quadprog and the barrier method of Gurobi these two techniques are almost the same.
For more details and information about this subject, I suggest you to see links and attached file on topic.
https://www.gurobi.com/documentation/9.0/refman/barqcpconvtol.html
https://www.researchgate.net/publication/239588219_Self-Scaled_Barriers_and_Interior-Point_Methods_for_Convex_Programming
https://cran.r-project.org/web/views/Optimization.html
https://www.researchgate.net/publication/260721127_An_Accelerated_Dual_Gradient-Projection_Algorithm_for_Embedded_Linear_Model_Predictive_Control
Best regards
Thanks for your answer.
Could you highlight the differences between the interior-point-convex of quadprog and the barrier method of Gurobi as you say these two techniques are almost the same? Especially about Gurobi I could not find much about which kind of matrices he can handle the best?
About quadprog I found the following:
The algorithm has different implementations for a sparse Hessian matrix H and for a dense matrix. Generally, the sparse implementation is faster on large, sparse problems, and the dense implementation is faster on dense or small problems.
Furthermore, about the convergence I found barely anything: Furthermore, which solver needs more iterations (with less expensive cost per iteration) and which solver needs fewer iterations, but expensive cost/time per iteration.
And I found in one of the articles you said, the following: However, interior-point methods are not easily warm started and do not scale well for very large problems .
What do they exactly mean with warm start? And what kind of scaling?
If you could tell me, it would be very helpful!
Dear Mohamed,
Quadprog and Gurobi give me the same objective function value and optimized values x, but GPAD gives me the same optimized values x, but an objective function value, which is a factor 10 bigger compared to quadprog and Gurobi. Do you know a possible explanation for this?
Furthermore, from my results, it seems that a simulation of the sparse formulation using Gurobi, the computation time scales quadratically with N and not linearly with N. What could be a possible explanation for this?
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