Undergraduate Convexity: From Fourier And Motzkin To Kuhn And Tucker, 1st Edition

  • Published By: World Scientific Publishing Company
  • ISBN-10: 981441252X
  • ISBN-13: 9789814412520
  • DDC: 515.8
  • Grade Level Range: College Freshman - College Senior
  • 300 Pages | eBook
  • Original Copyright 2013 | Published/Released January 2015
  • This publication's content originally published in print form: 2013

  • Price:  Sign in for price



Based on the widely used finite element method (FEM) and the latest Meshfree methods, a next generation of numerical method called Smoothed Point Interpolation Method (S-PIM) has been recently developed. The S-PIM is an innovative and effective combination of the FEM and the meshfree methods, and enables automation in computation, modeling and simulations - one of the most important features of the next generation methods. This important book describes the various S-PIM models in a systematic, concise and easy-to-understand manner. The underlying principles for the next generation of computational methods, G space theory, novel weakened weak (W2) formulations, techniques for shape functions, formulation procedures, and implementation strategies are presented in detail. Numerous examples are provided to demonstrate the efficiency and accuracy of the S-PIM solutions in comparison with the FEM and other existing methods. Effective techniques to compute solution bounds employing both S-PIM and FEM are highlighted to obtain certified solutions with both upper and lower bounds.The book also presents a systematically way to conduct adaptive analysis for solutions of desired accuracy using these bound properties, which is another key feature of the next generation of computational methods. This will benefit researchers, engineers and students who are venturing into new areas of research and computer code development. Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
1: Fourier-Motzkin Elimination.
2: Affine Subspaces.
3: Convex Subsets.
4: Polyhedra.
5: Computations with Polyhedra.
6: Closed Convex Subsets and Separating Hyperplanes.
7: Convex Functions.
8: Differentiable Functions of Several Variables.
9: Convex Functions of Several Variables.
10: Convex Optimization.
Linear (in)dependence and the Rank of a Matrix.