In many optimization problems arising from scientific, engineering and artificial intelligence
applications, objective and constraint functions are available only as the output of a black …

In this paper, we introduce a new stochastic approximation type algorithm, namely, the
randomized stochastic gradient (RSG) method, for solving an important class of nonlinear …

We present global convergence rates for a line-search method which is based on random
first-order models and directions whose quality is ensured only with certain probability. We …

We analyze Newton's method with lazy Hessian updates for solving general possibly non-
convex optimization problems. We propose to reuse a previously seen Hessian for several …

Do you know the difference between an optimist and a pessimist? The former believes we
live in the best possible world, and the latter is afraid that the former might be right.… In that …

In this paper, we present a new framework of bi-level unconstrained minimization for
development of accelerated methods in Convex Programming. These methods use …

A regularization algorithm using inexact function values and inexact derivatives is proposed
and its evaluation complexity analyzed. This algorithm is applicable to unconstrained …

This paper examines worst-case evaluation bounds for finding weak minimizers in
unconstrained optimization. For the cubic regularization algorithm, Nesterov and Polyak …

Derivative-free algorithms seek the minimum value of a given objective function without
using any derivative information. The performance of these methods often worsens as the …

In this paper, we prove that the broad class of direct-search methods of directional type
based on imposing sufficient decrease to accept new iterates shares the worst case …