QCQP

[blegat]

We could implement a PolyJuMP.QCQP.Optimizer meta-solver that is parametrized by a QCQP optimizer like Alpine or Gurobi and rewrites polynomial constraints into QCQP.
@matbesancon gave me the reference https://hal.science/hal-03795395/ during the JuMP-dev call that might be relevant

[matbesancon]

sorry note that the one of yesterday is only for polynomial binary optimization

[blegat]

@joaquimg I think you mentioned to me a paper in Boston this summer but I forgot :-P
@Shuvomoy What is the heuristic you use to rewrite monomials into quadratic in https://github.com/Shuvomoy/BnB-PEP-code ?

[Shuvomoy]

@blegat @joaquimg It was something like this: suppose we have $$x^3 y z = w,$$ then we introduce dummy variables $$p=x^2, v=yz, u = p x = x^3.$$ Then the original constraint $$x^3 y z = w \Leftrightarrow ( w = u v, p = x^2, u = p x, v = y z).$$

In BnB-PEP, there was only one degree 3 term due to problem structure, so the dummy variable assignment could be done mechanically.

[Shuvomoy]

We could implement a PolyJuMP.QCQP.Optimizer meta-solver that is parametrized by a QCQP optimizer like Alpine or Gurobi and rewrites polynomial constraints into QCQP. @matbesancon gave me the reference https://hal.science/hal-03795395/ during the JuMP-dev call that might be relevant

I think this will be a great idea. Especially, Gurobi's QCQP solver has gotten very good since it came out in 2019.

[blegat]

Closed by #95