In view of training increasingly complex learning architectures, we establish a nonsmooth
implicit function theorem with an operational calculus. Our result applies to most practical …

A new method for evaluating generalized derivatives in nonsmooth problems is reviewed.
Lexicographic directional (LD-) derivatives are a recently developed tool in nonsmooth …

Abstract The\emph {Cheap Gradient Principle}~\citep {Griewank: 2008: EDP: 1455489}---the
computational cost of computing a $ d $-dimensional vector of partial derivatives of a scalar …

A novel subgradient evaluation method is proposed for nonsmooth convex relaxations of
parametric solutions of ordinary differential equations (ODEs) arising in global dynamic …

Several chemical engineering applications demand global optimization of nonconvex
process models, including safety verification and determination of thermodynamic equilibria …

This paper extends classical sensitivity results for nonlinear programs to cases in which
parametric perturbations cause changes in the active set. This is accomplished using …

Graph centrality measures have found widespread use ranking agents in networks by
characterizing their “importance” for the purpose of predicting and managing network …

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 …

Using the notion of conservative gradient, we provide a simple model to estimate the
computational costs of the backward and forward modes of algorithmic differentiation for a …

This article proposes new practical methods for furnishing generalized derivative information
of optimal-value functions with embedded parameterized convex programs, with potential …