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15
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 612 (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 quadratic programming, semidefinite programming, and nonconvex and nonlinear problems, have reached varying levels of maturity. We review some of the key developments in the area, including comments on both the complexity theory and practical algorithms for linear programming, semidefinite programming, monotone linear complementarity, and convex programming over sets that can be characterized by selfconcordant barrier functions.
A simplified homogeneous and selfdual linear programming algorithm and its implementation
 Annals of Operations Research
, 1996
"... 1 Introduction Consider the linear programming (LP) problem in the standard form: (LP) minimize cT x ..."
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Cited by 61 (5 self)
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1 Introduction Consider the linear programming (LP) problem in the standard form: (LP) minimize cT x
Combining InteriorPoint and Pivoting Algorithms for Linear Programming
 Management Science
, 1996
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Approximate Farkas Lemmas and Stopping Rules for Iterative InfeasiblePoint Algorithms for Linear Programming
, 1996
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Y.CPark. A minimax approach for the joint design of acoustic crosstalk cancellation filters
 IEEE Transactions on Audio, Speech and Language Processing
, 2007
"... Abstract—This paper presents a method for jointly designing immersive audio rendering filters for a single listener using loudspeakers. The filters for crosstalk cancellation are assumed to have finite impulse responses and are designed using the minimax criterion. In addition to the traditional At ..."
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Abstract—This paper presents a method for jointly designing immersive audio rendering filters for a single listener using loudspeakers. The filters for crosstalk cancellation are assumed to have finite impulse responses and are designed using the minimax criterion. In addition to the traditional Atal–Schroeder crosstalk canceler structure, this paper explores an alternate topology that requires the approximation of a single filter. In general, the minimax approach provides improved lowfrequency performance leading to a better overall separation of the directpath and crosspath transfer functions than leastsquares designs. The performance of the singlefilter structure is better than that of the traditional crosstalk cancellation structure. Index Terms—Acoustic signal processing, crosstalk, loudspeakers, minimax methods. I.
A computational study of the homogeneous algorithm for largescale convex optimization
, 1996
"... Key words: Monotone complementarity problem, homogeneous and selfdual model, interiorpoint algorithms, largescale convex optimization. 1 Introduction In 1984 Karmarkar [31] presented an interiorpoint method for linear programming (LP) and since then interiorpoint algorithms enjoyed great public ..."
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Key words: Monotone complementarity problem, homogeneous and selfdual model, interiorpoint algorithms, largescale convex optimization. 1 Introduction In 1984 Karmarkar [31] presented an interiorpoint method for linear programming (LP) and since then interiorpoint algorithms enjoyed great publicity for two reasons. First, these algorithms solve LP problems in polynomial time, as proved by Karmarkar and many others. Secondly, interiorpoint algorithms have demonstrated excellent practical performance when solving largescale LP problems, see Lustig et al. [37]. It was soon realized (see Gill et al. [25]) that Karmarkar's method was closely related to the logarithmic barrier algorithm for general nonlinear programming studied by Fiacco and McCormick [23] and others in the sixties. Hence, it is natural to investigate the efficiency of the interiorpoint methods for solving more general classes of problems. In general good complexity results could only be expected for solving convex optimization problems.