line search method

An efficient penalty decomposition algorithm for minimization over sparse symmetric sets

  • Ahmad Mousavi
  • Morteza Kimiaei
  • Saman Babaie-Kafaki
  • Vyacheslav Kungurtsev
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems approximately via a two-block decomposition scheme: the first subproblem admits a closed-form solution without sparsity constraints, while the second subproblem is handled through an efficient … Read more

    Descent Scheme for a Class of Bilevel Programming Problems

  • Bhuvnesh Khatana
    • Categories Approximation Algorithms, Combinatorial Optimization, Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    In this paper, a class of bilevel programming problems is studied, in which the lower level is a quadratic programming problem, and the upper level problem consists of a nonlinear objective function with coupling constraints. An iterative process is developed to generate a sequence of points, which converges to the solution of this problem. In … Read more

    An improved randomized algorithm with noise level tuning for large-scale noisy unconstrained DFO problems

  • Morteza Kimiaei
    • Categories Optimization Software Benchmark, Stochastic Programming, Unconstrained Optimization Tags , , , ,

    In this paper, a new randomized solver (called VRDFON) for noisy unconstrained derivative-free optimization (DFO) problems is discussed. Complexity result in the presence of noise for nonconvex functions is studied. Two effective ingredients of VRDFON are an improved derivative-free line search algorithm with many heuristic enhancements and quadratic models in adaptively determined subspaces. Numerical results … Read more