@article{MathieuCardereraPokutta, author = {Mathieu, Besan{\c{c}}on and Carderera, Alejandro and Pokutta, Sebastian}, title = {FrankWolfe.jl: a high-performance and flexible toolbox for Frank-Wolfe algorithms and Conditional Gradients}, series = {INFORMS Journal on Computing}, volume = {34}, journal = {INFORMS Journal on Computing}, number = {5}, doi = {10.1287/ijoc.2022.1191}, pages = {2383 -- 2865}, abstract = {We present FrankWolfe.jl, an open-source implementation of several popular Frank-Wolfe and conditional gradients variants for first-order constrained optimization. The package is designed with flexibility and high performance in mind, allowing for easy extension and relying on few assumptions regarding the user-provided functions. It supports Julia's unique multiple dispatch feature, and it interfaces smoothly with generic linear optimization formulations using MathOptInterface.jl.}, language = {en} } @article{CardereraPokutta, author = {Carderera, Alejandro and Pokutta, Sebastian}, title = {Second-order Conditional Gradient Sliding}, abstract = {Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained quadratic subproblem at every iteration. We present the \emph{Second-Order Conditional Gradient Sliding} (SOCGS) algorithm, which uses a projection-free algorithm to solve the constrained quadratic subproblems inexactly. When the feasible region is a polytope the algorithm converges quadratically in primal gap after a finite number of linearly convergent iterations. Once in the quadratic regime the SOCGS algorithm requires O(log(log1/ε)) first-order and Hessian oracle calls and O(log(1/ε)log(log1/ε)) linear minimization oracle calls to achieve an ε-optimal solution. This algorithm is useful when the feasible region can only be accessed efficiently through a linear optimization oracle, and computing first-order information of the function, although possible, is costly.}, language = {en} }