AI4OPT / AI4OPT/PGLearn.jl

Support quadratic objectives

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Description

Supporting quadratic objectives should be fine with (most) solvers, it's more about getting the math right (especially for conic formulations).

We have two possibilities:
* pass the objective as quadratic, which would keep the same dual variables as we have now, but will introduce primal variables (namely `pg`) in the dual formulation
* cast the quadratic objective as a rotated SOC constraint, which it is slightly more cumbersome (especially if the solver supports quadratic objectives) but has the advantage of making the dual formulation self-contained. Doing that will introduce an additional dual variable, though.

Solver-wise: Gurobi, Clarabel and Ipopt support quadratic objectives. I believe HiGHS should support quadratic objectives, but I don't have any experience with its QP solver. Mosek does not support quadratic objectives.

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