Newton-conjugate gradient method

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, Unconstrained Optimization 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

    A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization

  • Chuan He
  • Zhaosong Lu
    • Categories Cone Programming, Nonlinear Optimization Tags , , , , , ,

    In this paper we consider finding an approximate second-order stationary point (SOSP) of general nonconvex conic optimization that minimizes a twice differentiable function subject to nonlinear equality constraints and also a convex conic constraint. In particular, we propose a Newton-conjugate gradient (Newton-CG) based barrier-augmented Lagrangian method for finding an approximate SOSP of this problem. Under … Read more

    A Newton-CG based augmented Lagrangian method for finding a second-order stationary point of nonconvex equality constrained optimization with complexity guarantees

  • Chuan He
  • Zhaosong Lu
  • Ting Kei Pong
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    In this paper we consider finding a second-order stationary point (SOSP) of nonconvex equality constrained optimization when a nearly feasible point is known. In particular, we first propose a new Newton-CG method for finding an approximate SOSP of unconstrained optimization and show that it enjoys a substantially better complexity than the Newton-CG method [56]. We … Read more

    A Newton-CG based barrier method for finding a second-order stationary point of nonconvex conic optimization with complexity guarantees

  • Chuan He
  • Zhaosong Lu
    • Categories Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , ,

    In this paper we consider finding an approximate second-order stationary point (SOSP) of nonconvex conic optimization that minimizes a twice differentiable function over the intersection of an affine subspace and a convex cone. In particular, we propose a Newton-conjugate gradient (Newton-CG) based barrier method for finding an $(\epsilon,\sqrt{\epsilon})$-SOSP of this problem. Our method is not … Read more