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Interiorpoint Methods
, 2000
"... The modern era of interiorpoint methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadrati ..."
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Cited by 607 (15 self)
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The modern era of interiorpoint methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex
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 ..."
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Cited by 18 (0 self)
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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
Interior Point Methods
"... The interior point method for linear programming was introduced by Karmakar in 1984. It runs in polynomial time and is a practical method. For many problems it is competitive or superior to the simplex method. Many LP packages, e.g., CPLEX, offer a simplex as well as an interior point method. Links ..."
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The interior point method for linear programming was introduced by Karmakar in 1984. It runs in polynomial time and is a practical method. For many problems it is competitive or superior to the simplex method. Many LP packages, e.g., CPLEX, offer a simplex as well as an interior point method. Links
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 548 (12 self)
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to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a
An InteriorPoint Method for Semidefinite Programming
, 2005
"... We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as maxcut. Other appli ..."
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Cited by 252 (19 self)
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We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as maxcut. Other
Interior Point Methods For Global Optimization
 INTERIOR POINT METHODS OF MATHEMATICAL PROGRAMMING
, 1996
"... Interior point methods, originally invented in the context of linear programming, have found a much broader range of applications, including global optimization problems that arise in engineering, computer science, operations research, and other disciplines. This chapter overviews the conceptual bas ..."
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Cited by 4 (1 self)
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Interior point methods, originally invented in the context of linear programming, have found a much broader range of applications, including global optimization problems that arise in engineering, computer science, operations research, and other disciplines. This chapter overviews the conceptual
Interior point methods in function space
 SIAM J. Control Optim
"... Abstract. A primaldual interior point method for optimal control problems is considered. The algorithm is directly applied to the infinitedimensional problem. Existence and convergence of the central path are analyzed, and linear convergence of a shortstep pathfollowing method is established. Ke ..."
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Cited by 21 (3 self)
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Abstract. A primaldual interior point method for optimal control problems is considered. The algorithm is directly applied to the infinitedimensional problem. Existence and convergence of the central path are analyzed, and linear convergence of a shortstep pathfollowing method is established
Barrier Functions in Interior Point Methods
 MATHEMATICS OF OPERATIONS RESEARCH
, 1996
"... We show that the universal barrier function of a convex cone introduced by Nesterov and Nemirovskii is the logarithm of the characteristic function of the cone. This interpretation demonstrates the invariance of the universal barrier under the automorphism group of the underlying cone. This provides ..."
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Cited by 57 (3 self)
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. This provides a simple method for calculating the universal barrier for homogeneous cones. We identify some known barriers as the universal barrier scaled by an appropriate constant. We also calculate some new universal barrier functions. Our results connect the field of interior point methods to several
• Barrier and Interior Point Methods
"... – Due Friday December 17, submit to Donna Ko (253 Cory) – Include background, motivation, problem formulation, methods, results (positive and negative), future directions – Aim to be intelligible to those without the technical background • Project posters (10–15 slidelike pages) – Poster session (t ..."
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– Due Friday December 17, submit to Donna Ko (253 Cory) – Include background, motivation, problem formulation, methods, results (positive and negative), future directions – Aim to be intelligible to those without the technical background • Project posters (10–15 slidelike pages) – Poster session
INTERIOR POINT METHODS FOR COMBINATORIAL OPTIMIZATION
, 1995
"... Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivale ..."
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Cited by 16 (9 self)
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Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem
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