Advances in Mathematical Methods and High Performance Computing

Intro
 Preface
 Contents
 Part I Mathematical Modeling, Applications, and Theoretical Foundations
 Canonical Duality-Triality Theory: Unified Understanding for Modeling, Problems, and NP-Hardness in Global Optimizationof Multi-Scale Systems
 1 Introduction and Motivation
 2 Multi-Scale Modeling and Properly Posed Problems
 2.1 Objectivity, Isotropy, and Symmetry in Modeling
 2.2 Subjectivity, Symmetry Breaking, and Well-Posed Problem
 2.3 Management Optimization
 2.4 Nonconvex Analysis and Boundary-Value Problems
 2.5 Lagrangian Mechanics and Initial-Value Problems 2.6 Mono-Duality and Duality Gap2.7 Bi-Duality and Conceptual Mistakes
 3 Unified Problem and Canonical Duality-Triality Theory
 3.1 Canonical Transformation and Gap Function
 3.2 Complementary-Dual Principle and Analytical Solution
 3.3 Triality Theory and NP-Hard Criterion
 4 Applications in Complex Systems
 4.1 Unconstrained Nonconvex Optimization Problem
 4.2 D.C. Programming
 4.3 Fixed Point Problems
 4.4 Mixed Integer Nonlinear Programming (MINLP)
 4.5 General Knapsack Problem and Analytical Solution
 4.6 Bilevel Optimization and Optimal Control 4.7 Multi-Level Multi-Targets MINLP and Topology Optimization5 Symmetry, NP-Hardness, and Perturbation Methods
 6 Connections with Popular Methods and Techniques
 6.1 Relation with SDP Programming
 6.2 Relation to Reformulation-Linearization/Convexification Technique
 6.3 Relation to Composite Minimization
 7 Conclusions
 References
 Numerical Investigation of Stochastic Neural Field Equations
 1 Introduction
 2 Numerical Approximation
 3 Numerical Examples
 4 Conclusions
 References
 Nonstationary Signal Decomposition for Dummies
 1 Introduction 2 The Ensemble Empirical Mode Decomposition Algorithm2.1 Numerical Examples
 3 The Iterative Filtering Method
 3.1 Numerical Examples
 4 Conclusions and Outlook
 References
 Modeling the Socio-Economic Waste Generation Factors Using Artificial Neural Network: A Case Study of Gurugram (Haryana State, India)
 1 Introduction
 2 Materials and Methods
 2.1 Case Study Area
 2.2 Material and Methods
 2.2.1 Population (POP)
 2.2.2 Urban Population (URB)
 2.2.3 Literate Population (LIT)
 2.2.4 Per Capita Income (PCI)
 2.2.5 Municipal Solid Waste (MSW) Data
 2.2.6 Statistical Analysis of Data 2.2.7 Proposed Artificial Neural Network (ANN) Model3 Results
 4 Conclusion
 References
 Regularization of Highly Ill-Conditioned RBF Asymmetric Collocation Systems in Fractional Models
 1 Introduction
 2 Preliminaries
 2.1 Fractional Integrals and Derivatives
 2.2 RBF Approximation
 3 Methodology
 3.1 A Fractional RBF Approximation
 3.2 Tikhonov Regularization
 3.3 Variable Shape Parameter
 4 Numerical Illustrations
 5 Conclusions
 References
 The Effect of Toxin and Human Impact on Marine Ecosystem
 1 Introduction
 2 The Mathematical Model 1
 3 Some Preliminary Results