text: The objectives of this technical report is to provide additional results on the generalized conditional gradient methods introduced by [BLM05]. Indeed , when the objective function is smooth, we provide a novel certificate of optimality and we show that the algorithm has a linear convergence rate. Applications of this algorithm are also discussed.
  @cite_21: Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo--Lampariello--Lucidi nonmonotone line search. In particular, the nonmonotone strategy is combined with the spectral gradient choice of steplength to accelerate the convergence process. In addition to the classical projected gradient nonlinear path, the feasible spectral projected gradient is used as a search direction to avoid additional trial projections during the one-dimensional search process. Convergence properties and extensive numerical results are presented.
summary: Finally our approach is also closely related to projected gradient descent and its spectral variant @cite_21 . As discussed more in detail in section , when @math is an euclidean distance, the solving problem boils down to a projection onto the convex @math . In practice the method is more general since it can be used for any problem as long as problem can be efficiently solved.