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Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms / / Jiming Peng, Cornelis Roos, Tamás Terlaky



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Autore: Peng Jiming Visualizza persona
Titolo: Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms / / Jiming Peng, Cornelis Roos, Tamás Terlaky Visualizza cluster
Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2009]
©2003
Edizione: Course Book
Descrizione fisica: 1 online resource (201 p.)
Disciplina: 519.6
Soggetto topico: Interior-point methods
Mathematical optimization
Programming (Mathematics)
Civil & Environmental Engineering
Engineering & Applied Sciences
Operations Research
Soggetto non controllato: Accuracy and precision
Algorithm
Analysis of algorithms
Analytic function
Associative property
Barrier function
Binary number
Block matrix
Combination
Combinatorial optimization
Combinatorics
Complexity
Conic optimization
Continuous optimization
Control theory
Convex optimization
Delft University of Technology
Derivative
Differentiable function
Directional derivative
Division by zero
Dual space
Duality (mathematics)
Duality gap
Eigenvalues and eigenvectors
Embedding
Equation
Estimation
Existential quantification
Explanation
Feasible region
Filter design
Function (mathematics)
Implementation
Instance (computer science)
Invertible matrix
Iteration
Jacobian matrix and determinant
Jordan algebra
Karmarkar's algorithm
Karush–Kuhn–Tucker conditions
Line search
Linear complementarity problem
Linear function
Linear programming
Lipschitz continuity
Local convergence
Loss function
Mathematical optimization
Mathematician
Mathematics
Matrix function
McMaster University
Monograph
Multiplication operator
Newton's method
Nonlinear programming
Nonlinear system
Notation
Operations research
Optimal control
Optimization problem
Parameter (computer programming)
Parameter
Pattern recognition
Polyhedron
Polynomial
Positive semidefinite
Positive-definite matrix
Quadratic function
Requirement
Result
Scientific notation
Second derivative
Self-concordant function
Sensitivity analysis
Sign (mathematics)
Signal processing
Simplex algorithm
Simultaneous equations
Singular value
Smoothness
Solution set
Solver
Special case
Subset
Suggestion
Technical report
Theorem
Theory
Time complexity
Two-dimensional space
Upper and lower bounds
Variable (computer science)
Variable (mathematics)
Variational inequality
Variational principle
Without loss of generality
Worst-case complexity
Yurii Nesterov
Persona (resp. second.): RoosCornelis
TerlakyTamás
Note generali: Description based upon print version of record.
Nota di contenuto: Frontmatter -- Contents -- Preface -- Acknowledgments -- Notation -- List of Abbreviations -- Chapter 1. Introduction and Preliminaries -- Chapter 2. Self-Regular Functions and Their Properties -- Chapter 3. Primal-Dual Algorithms for Linear Optimization Based on Self-Regular Proximities -- Chapter 4. Interior-Point Methods for Complementarity Problems Based on Self- Regular Proximities -- Chapter 5. Primal-Dual Interior-Point Methods for Semidefinite Optimization Based on Self-Regular Proximities -- Chapter 6. Primal-Dual Interior-Point Methods for Second-Order Conic Optimization Based on Self-Regular Proximities -- Chapter 7. Initialization: Embedding Models for Linear Optimization, Complementarity Problems, Semidefinite Optimization and Second-Order Conic Optimization -- Chapter 8. Conclusions -- References -- Index
Sommario/riassunto: Research on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function. The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best known iteration bounds of IPMs. Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work.
Titolo autorizzato: Self-Regularity  Visualizza cluster
ISBN: 1-282-08760-6
9786612087608
1-4008-2513-X
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910777727403321
Lo trovi qui: Univ. Federico II
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Serie: Princeton Series in Applied Mathematics