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The Resource Advances in Mathematical Modeling, Optimization and Optimal Control

Advances in Mathematical Modeling, Optimization and Optimal Control

Label
Advances in Mathematical Modeling, Optimization and Optimal Control
Title
Advances in Mathematical Modeling, Optimization and Optimal Control
Creator
Contributor
Subject
Language
eng
Member of
Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Springer Optimization and Its Applications Ser.
Series volume
v.109
Advances in Mathematical Modeling, Optimization and Optimal Control
Label
Advances in Mathematical Modeling, Optimization and Optimal Control
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=4530171
Publication
Copyright
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Contents -- Introduction -- Bregman Distances in Inverse Problems and Partial Differential Equations -- 1 Introduction -- 2 Bregman Distances and Their Basic Properties -- 2.1 Examples of Bregman Distances -- 2.2 Bregman Distances and Duality -- 2.3 Bregman Distances and Fenchel Duality -- 2.4 Bregman Distances for One-Homogeneous Functionals -- 3 Applications in Inverse Problems and Imaging -- 3.1 Error Estimates -- 3.2 Asymptotics -- 3.3 Bregman Iterations and Inverse Scale Space Methods -- 4 Applications in Partial Differential Equations -- 4.1 Entropy Dissipation Methods for Gradient Systems -- 4.2 Lyapunov Functionals for Gradient Systems Out of Equilibrium -- 4.3 Doubly Nonlinear Evolution Equations -- 4.4 Error Estimates for Nonlinear Elliptic Problems -- 5 Further Developments -- 5.1 Uncertainty Quantification in Inverse Problems -- 5.2 Bregman Distances and Optimal Transport -- 5.3 Infimal Convolution of Bregman Distances -- References -- On Global Attractor for Parabolic Partial Differential Inclusion and Its Time Semidiscretization -- 1 Introduction -- 2 Definitions -- 3 Problem Definition -- 4 Pseudomonotonicity of Nemytskii Operator for A -- 5 Convergence of Semi-Discrete Scheme -- 6 Global Attractor for Time Continuous Problem -- 7 Global Attractor for the Time Discrete Problem -- 8 Upper-Semicontinuous Convergence of Attractors -- 9 Examples -- References -- Passive Control of Singularities by Topological Optimization: The Second-Order Mixed Shape Derivatives of Energy Functionals for Variational Inequalities -- 1 Introduction -- 1.1 Asymptotic Approximation for Variational Inequalities -- 2 Applications of Steklov-Poincaré Operators in Asymptotic Analysis -- 3 Asymptotic Analysis by Domain Decomposition Method -- 4 Asymptotic Analysis of Boundary Value Problems in Rings or Spherical Shells -- 4.1 Elasticity Boundary Value Problems
  • 4.2 Explicit form of the Operator B for the Laplacian in Two Spatial Dimensions -- 4.3 Explicit form of the Operator B for the Laplacian in Three Spatial Dimensions -- 4.4 Explicit form of the Operator B for Elasticity in Two Spatial Dimensions -- 4.5 Explicit form of the Operator B for Elasticity in Three Spatial Dimensions -- 4.6 Laplace Spherical Polynomials -- 5 Asymptotic Analysis of Steklov-Poincaré Operators in Reinforced Rings in Two Spatial Dimensions -- 5.1 Model Problem -- 5.2 Steklov-Poincaré Operator -- 5.3 Asymptotic Expansion -- 5.4 Extension to Linear Elasticity -- 6 Asymptotic Expansions of the Steklov-Poincaré Operators and Perturbations of Bilinear Forms in Particular Cases -- 7 Directional Differentiability of the Metric Projection onto Positive Cone in Fractional Sobolev Spaces -- 7.1 Metric Projection onto Positive Cone in H1/200(c) -- 8 Rectilinear Crack in Two Spatial Dimensions -- 8.1 Green Formulae and Steklov-Poincaré Operators -- 9 Shape and Topological Derivatives of Elastic Energy in Two Spatial Dimensions for an Inclusion -- 9.1 Shape and Topological Derivatives of the Energy Functional in ]R with Respect to the Inclusion } -- References -- Optimal Control for Applications in Medical and Rehabilitation Technology: Challenges and Solutions -- 1 Introduction -- 2 Mathematical Models for Motion Studies in Medical and Rehabilitation Engineering -- 2.1 Whole-Body Models of Humans -- 2.2 Including Neuromuscular Models in the Human Model -- 2.3 Modeling the Rehabilitation Device and Establishing a Combined Model -- 3 Mathematical Stability Criteria for Human Movement -- 3.1 ZMP Related Criteria -- 3.2 Lyapunov's First Method -- 3.3 Lyapunov's Second Method -- 3.4 Capture Point Stability Criteria -- 3.5 Angular Momentum -- 4 Formulation and Solution of Optimal Control Problems for Motion Generation
  • 4.1 Multi-Phase Hybrid Optimal Control Problems with Standard Criteria -- 4.2 Multi-Phase Hybrid Optimal Control Problems with Non-standard Criteria Related to Stability -- 4.3 Numerical Solution of Optimal Control Problems -- 5 Formulation and Solution of Inverse Optimal Control Problems for Analysis of Motions in Medical Applications -- 6 Model-Based Optimization for Physical Assistive Devices for Geriatric Patients -- 7 Optimization and Analysis of Motions with Lower Limb Prostheses -- 8 Model-Based Optimization for the Design of Lower Limb Exoskeletons -- 9 Optimization of Functional Electrical Stimulation for Walking Motions of Hemiplegic Patients -- 10 Stability Studies of Human Walking -- 11 Conclusion and Perspectives -- References -- Second-Order Optimality Conditions for Broken Extremals and Bang-Bang Controls: Theory and Applications -- 1 Introduction -- 2 Second-Order Optimality Conditions for Broken Extremals in the Simplest Problem in the Calculus of Variations -- 2.1 The Simplest Problem in the Calculus of Variations -- 2.2 Second-Order Optimality Conditions for Broken Extremals -- 3 Second-Order Optimality Conditions for Discontinuous Controls in the General Problem of the Calculus of Variations on a Fixed Time Interval -- 3.1 The General Problem in the Calculus of Variations on a Fixed Time Interval -- 3.2 First-Order Necessary Conditions -- 3.3 Second-Order Necessary Conditions -- 3.4 Second-Order Sufficient Conditions -- 4 The General Problem in the Calculus of Variations on a Variable Time Interval -- 4.1 Statement of the Problem -- 4.2 First-Order Necessary Conditions -- 4.3 Second-Order Necessary Conditions -- 4.4 Second-Order Sufficient Conditions -- 5 Second-Order Optimality Conditions for Bang-Bang Controls -- 5.1 Optimal Control Problems with Control Appearing Linearly
  • 5.2 Necessary Optimality Conditions: The Minimum Principle of Pontryagin et al. -- 5.3 Second-Order Necessary Optimality Conditions -- 5.4 Second-Order Sufficient Optimality Conditions (SSC) -- 6 Induced Optimization Problem for Bang-Bang Controls and the Verification of SSC -- 6.1 Formulation of the Induced Optimization Problem and Necessary Optimality Conditions -- 6.2 Second-Order Optimality Conditions for Bang-Bang Controls in Terms of the Induced Optimization Problem -- 6.3 Numerical Methods for Solving the Induced Optimization Problem -- 7 Numerical Example with Fixed Final Time: Optimal Control of the Chemotherapy of HIV -- 8 Numerical Example with Free Final Time: Time-Optimal Control of Two-Link Robots -- 9 Optimal Control Problems with Mixed Control-State Constraints and Control Appearing Linearly -- 9.1 Statement of the Problem and Transformed Control Problem -- 9.2 Numerical Example: Optimal Control of the Rayleigh Equation -- 10 Conclusion -- References
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http://library.link/vocab/discovery_link
{'f': 'http://opac.lib.rpi.edu/record=b4385348'}
Extent
1 online resource (205 pages)
Form of item
online
Isbn
9783319307855
Media category
computer
Media MARC source
rdamedia
Media type code
c
Sound
unknown sound
Specific material designation
remote

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