first-order black-box information

An optimal subgradient algorithm with subspace search for costly convex optimization problems

  • Masoud Ahookhosh
  • Arnold Neumaier
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , , , ,

    This paper presents an acceleration of the optimal subgradient algorithm OSGA \cite{NeuO} for solving convex optimization problems, where the objective function involves costly affine and cheap nonlinear terms. We combine OSGA with a multidimensional subspace search technique, which leads to low-dimensional problem that can be solved efficiently. Numerical results concerning some applications are reported. A … Read more

    An optimal subgradient algorithm for large-scale convex optimization in simple domains

  • Masoud Ahookhosh
  • Arnold Neumaier
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , , , ,

    This paper shows that the optimal subgradient algorithm, OSGA, proposed in \cite{NeuO} can be used for solving structured large-scale convex constrained optimization problems. Only first-order information is required, and the optimal complexity bounds for both smooth and nonsmooth problems are attained. More specifically, we consider two classes of problems: (i) a convex objective with a … Read more