A01=Cornelis Roos
A01=Jiming Peng
A01=Tamas Terlaky
Algorithm
Analysis of algorithms
Analytic function
Associative property
Author_Cornelis Roos
Author_Jiming Peng
Author_Tamas Terlaky
Barrier function
Block matrix
Category=PBU
Category=PBW
Combinatorial optimization
Combinatorics
Complexity
Conic optimization
Continuous optimization
Control theory
Convex optimization
Delft University of Technology
Derivative
Duality gap
Eigenvalues and eigenvectors
Embedding
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Estimation
Explanation
Feasible region
Filter design
Function (mathematics)
Implementation
Instance (computer science)
Invertible matrix
Iteration
Jacobian matrix and determinant
Jordan algebra
Karush-Kuhn-Tucker conditions
Linear complementarity problem
Linear programming
Lipschitz continuity
Local convergence
Loss function
Mathematical optimization
Matrix function
McMaster University
Monograph
Multiplication operator
Newton's method
Nonlinear programming
Optimal control
Optimization problem
Parameter
Pattern recognition
Polynomial
Quadratic function
Requirement
Result
Scientific notation
Self-concordant function
Sensitivity analysis
Simplex algorithm
Simultaneous equations
Singular value
Smoothness
Solution set
Solver
Special case
Technical report
Theorem
Theory
Time complexity
Variable (mathematics)
Variational inequality
Variational principle
Without loss of generality
Yurii Nesterov
Product details
- ISBN 9780691091938
- Weight: 28g
- Dimensions: 152 x 235mm
- Publication Date: 27 Oct 2002
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
Jiming Peng is Professor of Mathematics at McMaster University and has published widely on nonlinear programming and interior-points methods. Cornelis Roos holds joint professorships at Delft University of Technology and Leiden University. He is an editor of several journals, coauthor of more than 100 papers, and coauthor (with Tamas Terlaky and Jean-Philippe Vial) of "Theory and Algorithms for Linear Optimization". Tamas Terlaky is Professor in the Department of Computing and Software at McMaster University, founding Editor in Chief of "Optimization and Engineering", coauthor of more than 100 papers, and an editor of several journals and two books.
