Pham Thi Hoai

A new proximal gradient algorithm for solving mixed variational inequality problems with a novel explicit stepsize and applications

  • Pham Thi Hoai
    • Categories Complementarity and Variational Inequalities, Convex Optimization, Nonlinear Optimization Tags , , , ,

    In this paper, we propose a new algorithm for solving monotone mixed variational inequality problems in real Hilbert spaces based on proximal gradient method. Our new algorithm uses a novel explicit stepsize which is proved to be increasing to a positive limitation. This property plays an important role in improving the speed of the algorithm. … Read more

    DC programming approach for solving a class of bilevel partial facility interdiction problems

  • Pham Thi Hoai
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags

    We propose a new approach based DC programming for fnding a solution of the partial facility interdiction problem that belongs to the class of bilevel programming. This model was frst considered in the work of Aksen et al. [1] with a heuristic algorithm named multi-start simplex search (MSS). However, because of the big number of … Read more

    A Novel Stepsize for Gradient Descent Method

  • Pham Thi Hoai
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Nonlinear Optimization Tags , , , ,

    In this paper, we propose a novel stepsize for the classical gradient descent scheme to solve unconstrained nonlinear optimization problems. We are concerned with the convex and smooth objective without the globally Lipschitz gradient condition. Our new method just needs the locally Lipschitz gradient but still gets the rate $O(\frac{1}{k})$ of $f(x^k)-f_*$ at most. By … Read more