Second-order Conditional Gradients

Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to the quadratic convergence rates these methods enjoy when close to the optimum. These algorithms require the solution of a constrained quadratic subproblem at every iteration. In the case where the feasible region can only be accessed efficiently through a linear optimization oracle, and computing first-order information about the function, although possible, is costly, the coupling of constrained second-order and conditional gradient algorithms leads to competitive algorithms with solid theoretical guarantees and good numerical performance.