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 …

Local Fourier analysis is a useful tool for predicting and analyzing the performance of many
efficient algorithms for the solution of discretized PDEs, such as multigrid and domain …

We develop an algorithm for minimax problems that arise in robust optimization in the
absence of objective function derivatives. The algorithm utilizes an extension of methods for …

In this paper we study the minimization of a nonsmooth black-box type function, without
assuming any access to derivatives or generalized derivatives and without any knowledge …

For strongly convex objectives that are smooth, the classical theory of gradient descent
ensures linear convergence relative to the number of gradient evaluations. An analogous …

We present new methods for solving a broad class of bound-constrained nonsmooth
composite minimization problems. These methods are specially designed for objectives that …

We propose a manifold sampling algorithm for minimizing a nonsmooth composition f=h∘F,
where we assume h is nonsmooth and may be inexpensively computed in closed form and F …

We develop and solve a constrained optimization model to identify an integrable optics rapid-
cycling synchrotron lattice design that performs well in several capacities. Our model …

Derivative-free optimization (DFO) is the mathematical study of the optimization algorithms
that do not use derivatives. One branch of DFO focuses on model-based DFO methods …

Variational Analysis studies mathematical objects under small variations. With regards to
optimization, these objects are typified by representations of first-order or second-order …