Zexian Liu

A Limited Memory Subspace Minimization Conjugate Gradient Algorithm for Unconstrained Optimization

  • Zexian Liu
  • Yu-Hong Dai
  • Hongwei Liu
    • Categories Nonlinear Optimization Tags , , ,

    Subspace minimization conjugate gradient (SMCG) methods are a class of high potential iterative methods for unconstrained optimization. The orthogonality is an important property of linear conjugate gradient method. It is however observed that the orthogonality of gradients in linear conjugate gradient method is often lost, which usually causes the slow convergence of conjugate gradient method. … Read more

    Two efficient gradient methods with approximately optimal stepsizes based on regularization models for unconstrained optimization

  • Zexian Liu
  • Wangli Chu
  • Hongwei Liu
    • Categories Unconstrained Optimization Tags , , , ,

    It is widely accepted that the stepsize is of great significance to gradient method. Two efficient gradient methods with approximately optimal stepsizes mainly based on regularization models are proposed for unconstrained optimization. More exactly, if the objective function is not close to a quadratic function on the line segment between the current and latest iterates, … Read more

    Some Modified Fast Iteration Shrinkage Thresholding Algorithms with a New Adaptive Non-monotone Stepsize Strategy for Nonsmooth and Convex Minimization Problems

  • Hongwei Liu
  • Wang Ting
  • Zexian Liu
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    The ” fast iterative shrinkage-thresholding algorithm ” (FISTA) is one of the most famous first order optimization scheme, and the stepsize, which plays an important role in theoretical analysis and numerical experiment, is always determined by a constant related to the Lipschitz constant or by a backtracking strategy. In this paper, we design a new … Read more

    New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization

  • Hongwei Liu
  • Zhao Ting
  • Zexian Liu
    • Categories Applications - OR and Management Sciences Tags , , , ,

    In this paper, two new subspace minimization conjugate gradient methods based on p-regularization models are proposed, where a special scaled norm in p-regularization model is analyzed. Diffierent choices for special scaled norm lead to different solutions to the p-regularized subproblem. Based on the analyses of the solutions in a two-dimensional subspace, we derive new directions … Read more