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Linear-fractional programming

About: Linear-fractional programming is a research topic. Over the lifetime, 3957 publications have been published within this topic receiving 155637 citations.


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Book ChapterDOI
Hongtao Bai1, Lili He1, Yu Jiang1, Jin Wang2, Shanshan Jiang1 
06 Jul 2016
TL;DR: A Revised Simplex Method (RSM) on a GPU–Data Parallel Virtual Machine (DPVM) assigns different routines for CPU and GPU according to respective characteristics: Iteration control and minimum value obtained are completed by CPU and Matrix multiplication by DPVM.
Abstract: Matrix manipulation of Linear Programming (LP) problems is a performance bottleneck in Single Instruction Single Data (SIMD) pattern. While, GPU is specialized for this compute-intensive and highly parallel computation, which is exactly what graphics rendering is about, due to the Single Instruction Multiple Data (SIMD) architecture. This paper introduces a Revised Simplex Method (RSM) on a GPU–Data Parallel Virtual Machine (DPVM). It assigns different routines for CPU and GPU according to respective characteristics: Iteration control and minimum value obtained are completed by CPU and Matrix multiplication by DPVM. In detail, we carefully organize the data as 4-channel textures, and efficiently implement the computation using Fetch4 technology of pixel shader. Numerical experiments are presented to verify the practical value and performance of this algorithm. The results are very promising. In particular, they reveal that our method not only can get correct optimal solution, but also is sixty-six faster than a traditional method on CPU, near 2.5 times faster than a lasted released MATLAB when LP problem size reaches 1200.
01 Jan 2007
TL;DR: In this paper, a monotonic affine scaling trust region algorithm is proposed for nonconvex programming, which minimizes the exact l 1 penalty function. But it may be desirable to have more than one local minimizer since there may be many local minimizers.
Abstract: A monotonic decrease minimization algorithm can be desirable for nonconvex minimization since there may be more than one local minimizers A typical interior point algorithm for a convex programming problem does not yield monotonic improvement of the objective function value In this paper, a monotonic affine scaling trust region algorithm is proposed for nonconvex programming The proposed affine scaling trust region algorithm is described in the context of minimizing the exact l1 penalty function Affine scaling Newton steps are derived directly from the complementarity conditions A primal trust region subproblem is proposed for globalization A dual subproblem is formulated to facilitate dual variables updates; its solution yields decrease of the l1 function Global convergence of the proposed algorithm is established
01 Jan 1985
TL;DR: An iterative method for solving a class of linear programming problems whose constraints satisfy certain diagonal dominance condition is proposed, and it is shown to converge even when implemented in an asynchronous, distributed manner, and that its rate of convergence can be determined from the synchronization parameter.
Abstract: An iterative method for solving a class of linear programming problems whose constraints satisfy certain diagonal dominance condition is proposed. This method partitions the original linear program into subprograms where each subprogram corresponds uniquely to a variable of the problem. At each iteration, one of the sub-programs is solved by adjusting its corresponding variable, while the other variables are held constant. This philosophy of successively changing one variable at a time is reminiscent of the coordinate relaxation method. The algorithmic mapping underlying this method is shown to be monotone and contractive. Then, using the contractive property, the method is shown to converge even when implemented in an asynchronous, distributed manner, and that its rate of convergence can be determined from the synchronization parameter. An illustration example is given.
Journal ArticleDOI
TL;DR: A brief overview of the life of Leonid Kantorovich and his contribution to the fields of linear programming and ordered vector spaces can be found in this article, where the authors also present a survey of the literature about linear programming.
Abstract: This is a brief overview of the life of Leonid Kantorovich (1912–1986) and his contribution to the fields of linear programming and ordered vector spaces.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202323
202248
202121
202027
201929
201830