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 introductory chapter, we present a high-level description of optimization, blackbox
optimization, and derivative-free optimization. We introduce some basic optimization …

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 consider a class of smoothing methods for minimization problems where the feasible set
is convex but the objective function is not convex, not differentiable and perhaps not even …

This paper presents a finite-difference quasi-Newton method for the minimization of noisy
functions. The method takes advantage of the scalability and power of BFGS updating, and …

We propose a first order interior point algorithm for a class of non-Lipschitz and nonconvex
minimization problems with box constraints, which arise from applications in variable …

In this paper, we study the generalized subdifferentials and the Riemannian gradient
subconsistency that are the basis for non-Lipschitz optimization on embedded submanifolds …

Regularized minimization problems with nonconvex, nonsmooth, perhaps non-Lipschitz
penalty functions have attracted considerable attention in recent years, owing to their wide …

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 …

Trust-region methods are a broad class of methods for continuous optimization that found
application in a variety of problems and contexts. In particular, they have been studied and …