The AT&T<i>Korbx</i>® System
AT&T Technical JournalPublished 6 May 1989
Yun-Chian Cheng, David J. Houck, Junmin Liu, Marc S. Meketon, Lev Slutsman, Robert J. Vanderbei
Citations27
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
The AT&T KORBX system, which implements certain variants of the Karmarkar algorithm on a computer that has multiple processors, each capable of performing vector arithmetic, is described.
Abstract
This paper describes the AT&T KORBX system, which implements certain variants of the Karmarkar algorithm on a computer that has multiple processors, each capable of performing vector arithmetic. We provide an overview of the KORBX system that covers its optimization algorithms, the hardware architecture, and software implementation techniques. Performance is characterized for a variety of applications found in industry, government, and academia.
Keywords
Computer ScienceMathematics
COMBINATORICAA new polynomial-time algorithm for linear programming
4,840 Citations1984Narendra Karmarkar
A Primal-Dual Interior Point Algorithm for Linear Programming
489 Citations1989Masakazu Kojima, Shinji Mizuno +1 more
Mathematical ProgrammingInterior path following primal-dual algorithms. part I: Linear programming
488 Citations1989Renato D. C. Monteiro, Ilan Adler
A primal-dual interior point algorithm for linear programming problems which requires a total of O(n L) number of iterations to find the Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem.
MINOS 5.0 User's Guide.
450 Citations1983B. A. Murtagh, Michael A. Saunders
MINOS is a large-scale optimization system, for the solution of sparse linear and nonlinear programs, with features including a new basis package, automatic scaling of linear constraints, and automatic estimation of some or all gradients.
Mathematical ProgrammingAn implementation of Karmarkar's algorithm for linear programming
422 Citations1989Ilan Adler, Maurício G. C. Resende +2 more
Based on a continuous version of Karmarkar's algorithm, two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested and compares favorably with the simplex codeMinos 4.0.
AlgorithmicaA modification of karmarkar's linear programming algorithm
357 Citations1986Robert J. Vanderbei, Marc S. Meketon +1 more
A modification of Karmarkar's linear programming algorithm that uses a recentered projected gradient approach thereby obviating a priori knowledge of the optimal objective function value and proves that the algorithm converges.
Mathematical ProgrammingA variation on Karmarkar’s algorithm for solving linear programming problems
331 Citations1986Earl Barnes
The algorithm described here is a variation on Karmarkar’s algorithm for linear programming that applies to the standard form of a linear programming problem and produces a monotone decreasing sequence of values of the objective function.
Mathematical ProgrammingAffine-scaling for linear programs with free variables
56 Citations1989Robert J. Vanderbei
The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables and it is shown that the geometrically elegant feasibility algorithm proposed by Chandru and Kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix.
AT&T Technical JournalPower Series Variants of Karmarkar-Type Algorithms
30 Citations1989Narendra Karmarkar, Jeffrey C. Lagarias +2 more
Two power-series algorithms are described; one builds on the dualaffine scaling algorithm and the other on a primal-dual path-following algorithm that accelerate convergence by reducing the number of iterations.
AT&T Technical JournalParallel Algorithms for the AT&T<i>Korbx</i>® System
7 Citations1989Efthymios Housos, Chien‐Chung Huang +1 more
Algorithms that optimize the AT&T KORBX system performance for the solution of sparse and dense sets of linear equations and exploit data locality, concurrency, and vectorization are presented.