Preliminaries -- C Representing Functionals -- Application in Nonlinear Optimization -- Application in Vector Optimization -- Application in Set Optimization -- Basics of Deep Learning -- Deep Learning with Set-Valued Inputs.

Neural networks offer a promising tool for the analysis of nonlinear economies. In this paper, we derive conditions for the global stability of nonlinear rational expectations equilibria under neural network learning. We demonstrate the applicability of the conditions in analytical and numerical...

We investigate the generalized red refinement for n-dimensional simplices that dates back to Freudenthal (Ann Math 43(3):580–582, 1942) in a mixed-integer nonlinear program (MINLP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...

Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more...