Polynomial-time pivot rule for the active-set method

Determine whether there exists a polynomial-time pivot rule for the active-set method applied to strictly concave quadratic objective functions.

Background

The paper formulates the active-set method as a nonlinear generalization of the simplex method. Its running time depends on the pivot rule used to select improving directions and update the active constraint set. Although strictly concave quadratic programs admit efficient subproblem computations and are a central setting for active-set algorithms, the paper states that no polynomial running-time guarantee is known for all instances under a suitable pivot rule.