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A derivative-free trust-region algorithm for composite nonsmooth optimization

- G. N. Grapiglia, Jinyun Yuan, Y. Yuan
- Mathematics
- 1 July 2016

The derivative-free trust-region algorithm proposed by Conn et al. (SIAM J Optim 20:387–415, 2009) is adapted to the problem of minimizing a composite function $$\varPhi… Expand

Tensor Methods for Finding Approximate Stationary Points of Convex Functions.

- G. N. Grapiglia, Y. Nesterov
- Mathematics, Physics
- 13 July 2019

In this paper we consider the problem of finding $\epsilon$-approximate stationary points of convex functions that are $p$-times differentiable with $\nu$-H\"{o}lder continuous $p$th derivatives. We… Expand

Tensor Methods for Minimizing Functions with H\"{o}lder Continuous Higher-Order Derivatives

- G. N. Grapiglia, Y. Nesterov
- Physics
- 29 April 2019

In this paper we study $p$-order methods for unconstrained minimization of convex functions that are $p$-times differentiable with $\nu$-Holder continuous $p$th derivatives. We propose tensor schemes… Expand

Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality

- G. N. Grapiglia, J. Yuan, Y. Yuan
- Mathematics, Computer Science
- J. Optim. Theory Appl.
- 8 September 2016

TLDR

On inexact solution of auxiliary problems in tensor methods for convex optimization

- G. N. Grapiglia, Y. Nesterov
- Computer Science, Mathematics
- Optim. Methods Softw.
- 30 July 2019

TLDR

Regularized Newton Methods for Minimizing Functions with Hölder Continuous Hessians

- G. N. Grapiglia, Y. Nesterov
- Mathematics, Computer Science
- SIAM J. Optim.
- 21 March 2017

TLDR

Accelerated Regularized Newton Methods for Minimizing Composite Convex Functions

- G. N. Grapiglia, Y. Nesterov
- Mathematics, Computer Science
- SIAM J. Optim.
- 8 January 2019

TLDR

Globally Convergent Second-order Schemes for Minimizing Twice-differentiable Functions

- G. N. Grapiglia, Y. Nesterov
- Mathematics
- 18 July 2016

In this paper, we suggest new universal second-order methods for unconstrained minimization of twice-differentiable (convex or non-convex) objective function. For the current function, these methods… Expand

On the worst-case complexity of nonlinear stepsize control algorithms for convex unconstrained optimization

- G. N. Grapiglia, J. Yuan, Y. Yuan
- Mathematics, Computer Science
- Optim. Methods Softw.
- 1 May 2016

TLDR

On the Complexity of an Augmented Lagrangian Method for Nonconvex Optimization

- G. N. Grapiglia, Y. Yuan
- Mathematics
- 13 June 2019

In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we prove a complexity… Expand

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