[SparseRunner]

Thanks. Matching Gurobi is not feasible, but HiGHS wants those who depend on open-source solvers to be able to work with bigger models than is currently possible. Once HiGHS has a good interior point solver (for QP) - the main aim of this proposal - the vision is to develop a nonlinear programming solver.

[quanto]

In your expert opinion, what is Gurobi's edge? The foundational mathematical formulation for solvers has been known for decades. I have read that Gurobi has many heuristics that statistically work well against real world problems.

What are concrete technical challenges HiGHS needs to solve to bridge the gap with Gurobi?

(my academic background is in numerical analysis/scientific computing but I didn't specialize in writing optimizers)

[SparseRunner]

For interior point the key is writing a multicore matrix decomposition code that exploits sparsity and the range of problem structure that is encountered. For MIP it's having techniques to exploit the many different problem features that occur and ensuring that they are used intelligently.