Nonlinear Analysis and Global Optimization (Springer Optimization and Its Applications, 167)

✍ Scribed by Themistocles M. Rassias (editor), Panos M. Pardalos (editor)

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 484
• Edition: 1st ed. 2021
• Category: Library

✦ Synopsis

This contributed volumediscusses aspects of nonlinear analysis in which optimization plays an important role, as well as topics which are applied to the study of optimization problems. Topics include set-valued analysis, mixed concave-convex sub-superlinear Schroedinger equation, Schroedinger equations in nonlinear optics, exponentially convex functions, optimal lot size under the occurrence of imperfect quality items, generalized equilibrium problems, artificial topologies on a relativistic spacetime, equilibrium points in the restricted three-body problem, optimization models for networks of organ transplants, network curvature measures, error analysis through energy minimization and stability problems, Ekeland variational principles in 2-local Branciari metric spaces, frictional dynamic problems, norm estimates for composite operators, operator factorization and solution of second-order nonlinear difference equations, degenerate Kirchhoff-type inclusion problems, and more.

✦ Table of Contents

Preface
Contents
Friction Models in the Framework of Set-Valued and ConvexAnalysis
1 Introduction
2 The Approach of Moreau and Panagiotopoulos
3 Models of Frictions
4 Stability Analysis of a Two-Degree-of-Freedom Mechanical System
References
A Survey on Markov's Theorem on Zeros of Orthogonal Polynomials
1 Introduction
2 Main Result
3 Markov's Theorem and Its Descendants
4 Some Applications
4.1 Sharp Monotonicity Properties of the Zeros of Orthogonal Polynomials Derived from Corollary 3.4
4.2 Sharp Monotonicity Properties of the Zeros of Orthogonal Polynomials Derived from Corollary 3.5
4.3 Monotonicity of the Zeros of Classical Continuous Orthogonal Polynomials Derived from Corollary 3.1 (Markov's Theorem)
4.4 Sharp Monotonicity Properties of the Zeros of Classical Continuous Orthogonal Polynomials Derived from Corollary 3.3
4.5 Monotonicity of the Zeros of Classical Discrete Orthogonal Polynomials Derived from Corollary 3.1 (Markov's Theorem)
References
A Review of Two Network Curvature Measures
1 Introduction
2 Gromov-Hyperbolic Curvature
2.1 Topological Characteristics of Gromov-Hyperbolicity Measure
2.2 Gromov Curvature of Real-World Networks
2.3 Efficient Computation of Gromov Curvature
2.4 Algorithmic Implications of Small Gromov Curvature
2.5 Statistical Validation of Gromov Curvature via Scaled'' Version 3 Geometric Curvature 3.1 Basic Topological Concepts 3.2 Topological Association of Networks with a Complex 3.3 Defining Geometric Curvatures for Elementary Components of Given Graph 1-Complex-Based Geometric Curvature for a Pair of Nodes 2-Complex-Based Geometric Curvature for a Pair of Nodes Higher-Dimensional Geometric Curvature for a Pair of Nodes 3.4 Overall (Scalar) Curvature Value for a Network 3.5 Computation of Geometric Curvatures 3.6 Real-World Networks and Geometric Curvatures 3.7 Statistical Validations for all Curvature Measures 4 Two Applications of Curvature Analysis of Graphs 4.1 Detecting Critical Elementary Components of Networks 4.2 Detecting Change Points in Dynamic Networks 5 Conclusion References A Frictional Dynamic Thermal Contact Problem with Normal Compliance and Damage 1 Introduction 2 The Contact Problem 3 Proof of Theorem 1 4 Analysis of a Numerical Scheme 5 Numerical Computations References Mixed Concave–Convex Sub-Superlinear Schrödinger Equation: Survey and Development of Some New Cases 1 Introduction 2 The Stationary Problem 2.1 Mixed Sub-linear Defocusing Case 0<p<q<1 2.2 The Defocusing Sub-linear Case p=1, 0<q<1 2.3 The Mixed Sub-linear/Linear Case 0<p<1 and q=1 2.4 A Mixed Sub-linear Defocusing Case o<q<p<1 2.5 A Mixed Sub-linear/Super-Linear Defocusing Case 0<p<1<q 2.6 Mixed Super-Linear/Sub-linear Defocusing Case 0<q<1<p 2.7 Mixed Linear/Super-Linear Defocusing Case p=1 and q>1 2.8 Mixed Super-Linear/Linear Defocusing Case q=1 and p>1 2.9 Mixed Super-Linear/Super-Linear Defocusing Case 1<p<q 2.10 Mixed Super-Linear/Super-Linear Defocusing Case 1<q<p 3 Some Graphical Illustrations 3.1 Example 1: The Mixed Sub-linear Case 0<p<q<1 3.2 Example 2: The Mixed Linear/Sub-linear Case p=1 and 0<q<1 3.3 Example 3: The Mixed Sub-linear/Sub-linear Case 0<q<p<1 3.4 Example 4: The Mixed Sub-linear/Linear Case 0<p<1 and q=1 4 Conclusion References An Optimization Model for a Network of Organ Transplants with Uncertain Availability 1 Introduction 2 The Mathematical Model 3 Variational Inequality 4 Numerical Examples 4.1 Example 1 Example 1.2 4.2 Example 2 5 Conclusions References Algebraic Based Techniques as Decision Making Tools 1 Introduction 2 Preliminaries 3 Median Algebras 4 Median Homomorphisms as Consensus Procedures 4.1 Consensus Over Trees 4.2 Consensus Over Hypercube–Free Median Algebras 4.3 Consensus Over Weak Orders 5 Application 6 Conclusions References Norm Estimates for the Composite Operators 1 Introduction 2 Local Integrability 3 Global Integrability References A Variational Inequality Based Stochastic Approximation for Inverse Problems in Stochastic Partial Differential Equations 1 Introduction 2 Stochastic Approximation for Variational Inequalities 3 Stochastic Approximation for Inverse Problems 3.1 Optimization Formulation of the Inverse Problem 3.2 Discrete Formulas 4 Computational Experiments 5 Concluding Remarks References An Iterative Method for a Common Solution of Split Generalized Equilibrium Problems and Fixed Points of a Finite Family of Nonexpansive Mapping 1 Introduction 2 Preliminaries 3 The Proposed Method and Some Properties 4 Numerical Example 5 Conclusions References Periodic Solutions Around the Out-of-Plane Equilibrium Points in the Restricted Three-Body Problem with Radiation and Angular Velocity Variation 1 Introduction 2 Equations of Motion 3 Out-of-Plane Equilibrium Points 4 Spatial Periodic Orbits Around the Out-of-Plane Equilibria 4.1 The Analytical Approximation 4.2 The Numerical Approximation 5 Discussion and Conclusion References Optimal Lot Size with Partial Backlogging Under the Occurrence of Imperfect Quality Items 1 Introduction 2 Preliminaries 2.1 Assumptions 2.2 Notation 3 Model Formulation and Optimal Policy Determination 3.1 Cycle Length 3.2 Total Profit Formulation 3.3 Optimal Policy 3.4 Special Cases 4 Numerical Comparisons 5 Cost Penalty of Employing the EOQ with Partial Backorders 6 Conclusions Appendix References Error Analysis Through Energy Minimization and Stability Properties of Exponential Integrators 1 Introduction and Motivation 2 Exponential Integrators for Hamiltonian Systems 3 High-Order Exponential Variational Integrators 4 Stability Analysis of Exponential Variational Integrators 4.1 Exponential Variational Integrator for S=2 4.2 Exponential Variational Integrator for S=3 5 Error Analysis from Testing the Variational Integrators in Hamiltonian Systems 6 Conclusions References A Degenerate Kirchhoff-Type Inclusion Problem with NonlocalOperator 1 Introduction 2 Mathematical Background 3 Statement of Main Result 4 Truncated Problems 5 Mountain-Pass Geometry 6 Palais–Smale Condition 7 Proof of Theorem 2 and Example References Competition for Medical Supplies Under Stochastic Demand in the Covid-19 Pandemic: A Generalized Nash Equilibrium Framework 1 Introduction 2 Literature Review and Our Contributions 3 The Generalized Nash Equilibrium Network Model for Medical Supplies Under Stochastic Demand 3.1 Illustrative Examples 4 Qualitative Properties and the Algorithm The Modified Projection Method 5 Numerical Examples 6 Summary and Conclusions and Suggestions for Future Research References Relative Strongly Exponentially Convex Functions 1 Introduction 2 Preliminary Results 3 Main Results 4 Conclusion References Properties of Exponentially m-Convex Functions 1 Introduction 2 Preliminary Results 3 Main Results 4 Conclusion References Natural vs. Artificial Topologies on a Relativistic Spacetime 1 Motivation: The Topologization Problem 2 What Is (or Should be) the Role of Spacetime Topology? 3 Singularities, Naked Singularities and a Kind of Unexpected Gravitational Time Delay Effects 4 A Duality Between Timelike–Spacelike Events: BetweenChronos'' and ``Choros''
5 Questions
References
On the Approximation of Monotone Variational Inequalities in Lp Spaces with Probability Measure
1 Introduction
2 Regularization of Random Variational Inequalities
2.1 Random Variational Inequalities in Probabilistic Lebesgue Spaces
2.2 A Functional Approximation Scheme for the Random Variational Inequality
2.3 Implementation
3 Application to the Traffic Network Equilibrium Problem with Random Data
3.1 An Outline of the Traffic Network Equilibrium Problem
3.2 The Stochastic VI Formulation of the Traffic Network Equilibrium Problem
3.3 Numerical Experiments
References
Operator Factorization and Solution of Second-Order Nonlinear Difference Equations with Variable Coefficients and Multipoint Constraints
1 Introduction
2 Factorization Method
3 Second-Order Nonlinear Difference Equations
3.1 Type I
3.2 Type II
References
An Invitation to the Study of a Uniqueness Problem
Reference
Schrödinger Equations in Nonlinear Optics
1 Introduction
2 Some Lemmas
3 Proof of Theorem 2
4 Proof of Theorem 3
References
Ekeland Variational Principles in 2-Local Branciari Metric Spaces
1 Introduction
2 Dependent Choice Principles
3 Conv-Cauchy Structures
4 Local and 2-Local Branciari Metric Spaces
5 Main Result
6 Equivalence Statements
References