Mathematical Control and Numerical Applications : JANO13, Khouribga, Morocco, February 22–24, 2021

This book presents some sufficient mathematical content with expressive result. The aim of JANO13 is to bring together scientists to discuss their research in all the aspects of mathematics and their applications to different scientific discipline. The main topics of the conference is partial differential equations, mathematical control, numerical analysis and computer science. The conference is interested in recent developments on numerical analysis and real applications in computer science. The latter is viewed as a dynamic branch on the interface of mathematics and informatics that has been growing rapidly over the past several decades. However, its mathematical modelling and interpretation are still not well-explained and need much more clarifications. The main contributions of this book are to give some sufficient mathematical content with expressive results. As a growing field, it is gaining a lot of attention both in media and in the industry world, which will attract the interest of readers from different scientist disciplines. Preface Contents VRP with Flexible Time Windows Using the ALNS Metaheuristic Algorithm 1 Problem Formulation of the VRPFlexTW 2 ALNS State of the Art in the Context of VRP 3 ALNS Techniques for VRPFlexTW 4 Numerical Experiment 5 Conclusion References VRPTW: From Mathematical Models to Computing Science Tools 1 Introduction 2 Mathematical Formulation 3 Adaptive Large Neighborhood Search 4 Deterministic Vehicle Routing Problem with Time Windows (VRPTW) 4.1 The Modified Adaptive Large Neighborhood Search (MALNS) 4.2 The Multi-threading Parallel ALNS 5 Robust Vehicle Routing Problem with Time Windows (RVRPTW) 5.1 Sequential Approach to Solve the RVRPTW 5.2 Multi-threading Parallel Approach to Solve the RVRPTW 6 Computational Experiments 6.1 Computational Results of the MALNS 6.2 Computational Results of the Multi-threading Parallel ALNS 6.3 Computational Results of the Sequential Robust Approach 6.4 Computational Results of the Parallel Robust Approaches 7 Conclusion References An Anisotropic PDE for Multi-frame Super-Resolution Image Reconstruction 1 Multi-frame SR Model 2 Discritization and Numerical Result References Acceleration of the KMF Algorithm Convergence to Solve the Cauchy Problem for Poisson's Equation 1 Introduction 2 Cauchy Problem for Poisson's Equation and JN Relaxed Algorithm 2.1 The JN Relaxed Algorithm 3 Convergence Analysis 4 Acceleration of Convergence 5 Numerical Results 6 Conclusion References Identification of Genuine from Fake Banknotes Using an Enhanced Machine Learning Approach 1 Introduction 2 Formulating the Binary Classification Problem 2.1 Kernel Function 3 Hinge Loss Function 4 Experimental Results 4.1 Feature Importance 5 Conclusion References Identification of Robin Coefficient in Elliptic Problem by a Coupled Complex Boundary Method 1 Introduction 2 A Reformulation with CCBM 3 Tikhonov Regularization 4 Numerical Results 4.1 Identification Results Without Noise 4.2 Identification Results with Noise References A New Space-Variant Optimization Approach for Image Segmentation 1 Introduction 2 The Problem Formulation 3 The ADMM Algorithm 4 Numerical Results 5 Conclusion References A Lagrangian Mixed Finite Elements Method for Advection-Diffusion Equations 1 Introduction 2 Eulerian-Lagrangian Method 2.1 Lagrangian Discretization of the Advection Problem 2.2 Eulerian Discretization of the Diffusion Subproblem 2.3 Particle–Mesh Interaction 2.4 Mesh-Particle Projection 3 Numerical Experiments References Adaptation by Nash Games in Gradient-Based Multi-objective/Multi-disciplinary Optimization 1 Introduction 2 Nash-Game-Based Adaptation Algorithm 2.1 Mathematical Problem Definition 2.2 Convex Hull, Common Descent Direction and Directional Derivatives 2.3 Preliminary Calculations 2.4 Nash Game Formulation and Statement of Theoretical Result 3 Proof and Convergence Rate 3.1 Compatibility 3.2 Continuum of Nash Equilibria 3.3 Variation of the Primary Cost Functions Along the Continuum 3.4 Variation of the Secondary Cost Functions Along the Continuum 3.5 Secondary Cost Functions 4 Illustration of the Prioritized Multi-objective Optimization Approach 4.1 Numerical Implementation 4.2 Application to the Sizing of a Sandwich Element for Optimal Mechanical Resistance 5 Conclusion and Perspective References Blind Noisy Mixture Separation for Dependent Sources 1 Introduction 2 Problem Statement 3 First Step: Denoising of Observations 3.1 Regularization Total Variation 3.2 Discretization 3.3 Algorithme de Projection de Chambolle 4 Second Step: BSS Based on the Combination of Copula and TV 4.1 Case of Independent Sources 4.2 Case of Dependent Sources 5 Simulation Results 6 Conclusion References Blind Separation of Dependent Sources Using Copula 1 Introduction 2 Problem Statement 3 Copula 4 Case of Independent Sources 5 Case of Dependent Sources 5.1 Procedure 1: Dependent BSS Based on a Priori Knowledge on the Sources 5.2 Procedure 2: BSS for Dependent Sources When the Dependency Model Is Known and the Parameter Is Unknown 5.3 Procedure 3: BSS for Dependent Sources When the Dependency Model Is Unknown and the Parameter Is Unknown 6 Experimental Performance Study 6.1 Series 1: Tests with Various Types of Signals 6.2 Series 2: Tests with Images 7 Conclusion References