Nonlinear Algebra in an ACORN

A simple algorithm for solving a set of nonlinear equations by matrix algebra has been discovered recently — first by transforming them into an equivalent matrix equation and then finding the solution analytically in terms of the inverse matrix of this equation. With this newly developed ACORN (Adaptive Constrained Optimal Robust Nonlinear) algorithm, it is possible to minimize the objective function [constructed from the functions in the nonlinear set of equations] without computing its derivatives.

This book will present the details of ACORN algorithm and how it is used to solve large scale nonlinear equations with an innovative approach ACORN Magic [minimization algorithms gathered in a cloud].

The ultimate motivation of this work is its application to optimization. In recent years, with the advances in big-data, optimization becomes an even more powerful tool in knowledge discovery. ACORN Magic is the perfect choice in this kind of application because of that fact that it is fast, robust and simple enough to be embedded in any type of machine learning program.
Sample Chapter(s)
Foreword
Chapter 1: An Overview of Optimization

Contents:An Overview of OptimizationThe ACORN Approach to OptimizationApplication to Pedagogical ExamplesA Data-Modeling Example in Accelerator PhysicsApplications to Machine Learning and Neural NetworksAppendices:Code for Plotting the Basin of Attraction (BOA) in OctaveACORN Code Implementation in OctaveDetails for Optimizing the Objective Function in NN8Details for Optimizing the Objective Function in NN481
Readership: Students and researchers of optimization in solving nonlinear equations in scientific and engineering problems.
Optimization;ACORN;Nonlinear Equations;Neural Networks00