On fast convergence rates for generalized conditional gradient methods with backtracking stepsize

<p style='text-indent:20px;'>A generalized conditional gradient method for minimizing the sum of two convex functions, one them differentiable, is presented. This iterative relies on main ingredients: First, minimization a partially linearized objective functional to compute descent direction and, second, stepsize choice based an Armijo-like condition ensure sufficient in every iteration. We provide several convergence results. Under mild assumptions, generates sequences iterates which converge, subsequences, towards minimizers. Moreover, sublinear rate values derived. Second, we show that enjoys improved rates if problem fulfills certain growth estimates. Most notably these results do not require strong convexity functional. Numerical tests variety challenging PDE-constrained optimization problems confirm practical efficiency proposed algorithm.</p>