Results 1  10
of
47
A unified approach to interiorpoint algorithms for linear complementarity problems.
 Lecture Notes in Computer Science,
, 1991
"... ..."
(Show Context)
Semidefinite optimization
 Acta Numerica
, 2001
"... Optimization problems in which the variable is not a vector but a symmetric matrix which is required to be positive semidefinite have been intensely studied in the last ten years. Part of the reason for the interest stems from the applicability of such problems to such diverse areas as designing the ..."
Abstract

Cited by 149 (2 self)
 Add to MetaCart
(Show Context)
Optimization problems in which the variable is not a vector but a symmetric matrix which is required to be positive semidefinite have been intensely studied in the last ten years. Part of the reason for the interest stems from the applicability of such problems to such diverse areas as designing the strongest column, checking the stability of a differential inclusion, and obtaining tight bounds for hard combinatorial optimization problems. Part also derives from great advances in our ability to solve such problems efficiently in theory and in practice (perhaps “or ” would be more appropriate: the most effective computational methods are not always provably efficient in theory, and vice versa). Here we describe this class of optimization problems, give a number of examples demonstrating its significance, outline its duality theory, and discuss algorithms for solving such problems.
The many facets of linear programming
 Math. Program., 91(3, Ser. B):417–436, 2002. ISMP 2000, Part 1
"... ..."
InfeasibleStart PrimalDual Methods And Infeasibility Detectors For Nonlinear Programming Problems
 Mathematical Programming
, 1996
"... In this paper we present several "infeasiblestart" pathfollowing and potentialreduction primaldual interiorpoint methods for nonlinear conic problems. These methods try to find a recession direction of the feasible set of a selfdual homogeneous primaldual problem. The methods under ..."
Abstract

Cited by 38 (6 self)
 Add to MetaCart
(Show Context)
In this paper we present several "infeasiblestart" pathfollowing and potentialreduction primaldual interiorpoint methods for nonlinear conic problems. These methods try to find a recession direction of the feasible set of a selfdual homogeneous primaldual problem. The methods under consideration generate an fflsolution for an fflperturbation of an initial strictly (primal and dual) feasible problem in O( p ln fflae f ) iterations, where is the parameter of a selfconcordant barrier for the cone, ffl is a relative accuracy and ae f is a feasibility measure. We also discuss the behavior of pathfollowing methods as applied to infeasible problems. We prove that strict infeasibility (primal or dual) can be detected in O( p ln ae \Delta ) iterations, where ae \Delta is a primal or dual infeasibility measure. 1 Introduction Nesterov and Nemirovskii [9] first developed and investigated extensions of several classes of interiorpoint algorithms for linear programming t...
SelfScaled Cones and InteriorPoint Methods in Nonlinear Programming
 Working Paper, CORE, Catholic University of Louvain, LouvainlaNeuve
, 1994
"... : This paper provides a theoretical foundation for efficient interiorpoint algorithms for nonlinear programming problems expressed in conic form, when the cone and its associated barrier are selfscaled. For such problems we devise longstep and symmetric primaldual methods. Because of the special ..."
Abstract

Cited by 29 (2 self)
 Add to MetaCart
(Show Context)
: This paper provides a theoretical foundation for efficient interiorpoint algorithms for nonlinear programming problems expressed in conic form, when the cone and its associated barrier are selfscaled. For such problems we devise longstep and symmetric primaldual methods. Because of the special properties of these cones and barriers, our algorithms can take steps that go typically a large fraction of the way to the boundary of the feasible region, rather than being confined to a ball of unit radius in the local norm defined by the Hessian of the barrier. Key words: Nonlinear Programming, conical form, interior point algorithms, selfconcordant barrier, selfscaled cone, selfscaled barrier, pathfollowing algorithms, potentialreduction algorithms. AMS 1980 subject classification. Primary: 90C05, 90C25, 65Y20. CORE, Catholic University of Louvain, LouvainlaNeuve, Belgium. Email: nesterov@core.ucl.ac.be. Part of this work was done while the author was visiting the Cornell C...
Interiorpoint methods for optimization
, 2008
"... This article describes the current state of the art of interiorpoint methods (IPMs) for convex, conic, and general nonlinear optimization. We discuss the theory, outline the algorithms, and comment on the applicability of this class of methods, which have revolutionized the field over the last twen ..."
Abstract

Cited by 18 (0 self)
 Add to MetaCart
This article describes the current state of the art of interiorpoint methods (IPMs) for convex, conic, and general nonlinear optimization. We discuss the theory, outline the algorithms, and comment on the applicability of this class of methods, which have revolutionized the field over the last twenty years.
Application of barrier function base model predictive control to an edible oil refining process. Provisionally accepted for the Journal of Process Control
, 2004
"... March, 2003I hereby certify that the work embodied in this thesis is the result of original research and has not been submitted for a higher degree to any other University or Institution. Adrian WillsAcknowledgements I would like to thank my supervisor Dr. Will Heath for his exceptional patience, hi ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
March, 2003I hereby certify that the work embodied in this thesis is the result of original research and has not been submitted for a higher degree to any other University or Institution. Adrian WillsAcknowledgements I would like to thank my supervisor Dr. Will Heath for his exceptional patience, his willingness to sacrifice, his genuine and pragmatic approach to research and for his friendship which I hope continues. I am indebted to Will for more than I can recall and I am truly grateful for all of his help and support. Thanks. A special thanks to Dr. Liuping Wang, who helped establish my scholarship and the industrial partnership. A further special thanks to Professors Graham Goodwin and Rick Middleton for their technical and financial support. Thanks to Dr. Charlie Chessari and Jay Selahewa who established my scholarship through
A potentialfunction reduction algorithm for solving a linear program directly from an infeasible 'warm start
 Mathematical Programming 52
, 1991
"... ..."
(Show Context)
Projective Transformations for Interior Point Algorithms, and a Superlinearly Convergent Algorithm for the WCenter Problem
"... The purpose of this study is to broaden the scope of projective transformation methods in mathematical programming, both in terms of theory and algorithms. We start by generalizing the concept of the analytic center of a polyhedral system of constraints to the wcenter of a polyhedral system, which ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
(Show Context)
The purpose of this study is to broaden the scope of projective transformation methods in mathematical programming, both in terms of theory and algorithms. We start by generalizing the concept of the analytic center of a polyhedral system of constraints to the wcenter of a polyhedral system, which stands for weighted center, where there are positive weights on the logarithmic barrier terms for reach inequality constraint defining the polyhedron X. We prove basic results regarding contained and containing ellipsoids centered at the wcenter of the system X. We next shift attention to projective transformations, and we exhibit an elementary projective transformation that transforms the polyhedron X to another polyhedron Z, and that transforms the current interior point to the wcenter of the transformed polyhedron Z. We work throughout with a polyhedral system of the most general form, namely both inequality and equality costraints. This theory is then applied to the problem of finding the wcenter of a polyhedral system X. We present a projective transformation algorithm, which is