A logarithmic barrier approach for linear programming

Menniche, L.; Benterki, Djamel

doi:10.1016/j.cam.2016.05.025

Cited by 10 publications

(17 citation statements)

References 9 publications

(12 reference statements)

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“…In LBF technique, the search operation is performed in a continuous space domain to deduce the optimal points. Then, these points are discretized to obtain the optimal solution [26,27].…”

Section: Methodsmentioning

confidence: 99%

FPGA Implementation of an Improved Reconfigurable FSMIM Architecture Using Logarithmic Barrier Function Based Gradient Descent Approach

Das

Panchanathan

2019

International Journal of Reconfigurable Computing

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Recently, the Reconfigurable FSM has drawn the attention of the researchers for multistage signal processing applications. The optimal synthesis of Reconfigurable finite state machine with input multiplexing (Reconfigurable FSMIM) architecture is done by the iterative greedy heuristic based Hungarian algorithm (IGHA). The major problem concerning IGHA is the disintegration of a state encoding technique. This paper proposes the integration of IGHA with the state assignment using logarithmic barrier function based gradient descent approach to reduce the hardware consumption of Reconfigurable FSMIM. Experiments have been performed using MCNC FSM benchmarks which illustrate a significant area and speed improvement over other architectures during field programmable gate array (FPGA) implementation.

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“…In LBF technique, the search operation is performed in a continuous space domain to deduce the optimal points. Then, these points are discretized to obtain the optimal solution [26,27].…”

Section: Methodsmentioning

confidence: 99%

FPGA Implementation of an Improved Reconfigurable FSMIM Architecture Using Logarithmic Barrier Function Based Gradient Descent Approach

Das

Panchanathan

2019

International Journal of Reconfigurable Computing

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“…In the LBF method, optimization of the objective function is accomplished in the continuous space domain. The obtained analytic solution is then discretized to produce the exact discrete solution [24]. Thus, the objective function for LBF, which is subjected to inequality constraints, is defined by (17).…”

Section: Logarithmic Barrier Function Based Gradient Descentmentioning

confidence: 99%

“…Hence, the hypercube embedding problem is interpreted as determining -binary ]-vectors that minimizes (16). It is given in (24).…”

Section: Min ( )mentioning

confidence: 99%

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A Gradient‐Based Interior‐Point Method to Solve the Many‐to‐Many Assignment Problems

Das

Priya

2019

Complexity

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The many-to-many assignment problem (MMAP) is a recent topic of study in the field of combinatorial optimization. In this paper, a gradient-based interior-point method is proposed to solve MMAP. It is a deterministic method which assures an optimal solution. In this approach, the relaxation of the constraints is performed initially using the cardinality constraint detection operation. Then, the logarithmic barrier function (LBF) based gradient descent approach is executed to reach an accurate solution. Experiments have been performed to validate the practical implementation of the proposed algorithm. It also illustrates a significant improvement in convergence speed for the large MMAPs (i.e., if group size, α≥80) over state-of-the-art literature.

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“…Various approaches are developed to overcome this difficulty. It is known [2,6] that the computation of the step-size is expensive specifically while using line search methods. Leulmi and al.…”

Section: Introductionmentioning

confidence: 99%

Logarithmic Barrier Method Via Minorant Function for Linear Programming

Leulmi¹,

Soumia²

2019

J. Sib. Fed. Univ., Math. phys.

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We propose in this study, a new logarithmic barrier approach to solve linear programming problem. We are interested in computation of the direction by Newton's method and of the displacement step using minorant functions instead of line search methods in order to reduce the computation cost. Our new approach is even more beneficial than classical line search methods. This purpose is confirmed by many interesting numerical experimentations shown the effectiveness of the algorithm developed in this work.

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A logarithmic barrier approach for linear programming

Cited by 10 publications

References 9 publications

FPGA Implementation of an Improved Reconfigurable FSMIM Architecture Using Logarithmic Barrier Function Based Gradient Descent Approach

FPGA Implementation of an Improved Reconfigurable FSMIM Architecture Using Logarithmic Barrier Function Based Gradient Descent Approach

A Gradient‐Based Interior‐Point Method to Solve the Many‐to‐Many Assignment Problems

Logarithmic Barrier Method Via Minorant Function for Linear Programming

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