Junyu Zhang

Adaptive Newton-CG methods with global and local analysis for unconstrained optimization with Hölder continuous Hessian

  • Ziyang Zeng
  • Junyu Zhang
  • Chuan He
    • Categories Nonlinear Optimization, Other Topics Tags , , , ,

    In this paper, we study Newton-conjugate gradient (Newton-CG) methods for minimizing a nonconvex function $f$ whose Hessian is $(H_f,\nu)$-H\”older continuous with modulus $H_f>0$ and exponent \(\nu\in(0,1]\). Recently proposed Newton-CG methods for this problem \cite{he2025newton} adopt (i) non-adaptive regularization and (ii) a nested line-search procedure, where (i) often leads to inefficient early progress and the loss … Read more

    Stochastic Variance-Reduced Prox-Linear Algorithms for Nonconvex Composite Optimization

  • Lin Xiao
  • Junyu Zhang
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , ,

    We consider the problem of minimizing composite functions of the form $f(g(x))+h(x)$, where~$f$ and~$h$ are convex functions (which can be nonsmooth) and $g$ is a smooth vector mapping. In addition, we assume that $g$ is the average of finite number of component mappings or the expectation over a family of random component mappings. We propose … Read more