CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

Yang, Yaguang

doi:10.1007/s11075-016-0180-1

Cited by 13 publications

(28 citation statements)

References 39 publications

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“…The two proposed algorithms are very similar to the one in [16] in that they are all for solving linear programming of standard form using arc-search. Implementation strategies for the four algorithms (two proposed in this paper, one proposed in [16], and Mehrotra's algorithm described in [1]) are in common except algorithm-specific parameters (Section 6.1), selection of α k (Section 6.8 for arc-search), section of σ k (Section 6.9), and rescale α k (Section 6.10) for the two algorithms proposed in this paper. Most of these implementation strategies have been thoroughly discussed in [16].…”

Section: Implementation Detailsmentioning

confidence: 99%

“…Implementation strategies for the four algorithms (two proposed in this paper, one proposed in [16], and Mehrotra's algorithm described in [1]) are in common except algorithm-specific parameters (Section 6.1), selection of α k (Section 6.8 for arc-search), section of σ k (Section 6.9), and rescale α k (Section 6.10) for the two algorithms proposed in this paper. Most of these implementation strategies have been thoroughly discussed in [16]. Since all these strategies affect the numerical efficiency, we summarize all details implemented in this paper and explain the reasons why some strategies are adopted and some are not.…”

Section: Implementation Detailsmentioning

confidence: 99%

“…obtained by these two methods and select the initial point with smaller value of (72) as we guess this selection may reduce the number of iterations (see [16] for detail).…”

Section: Initial Point Selectionmentioning

confidence: 99%

“…Because the purpose of [16] is to demonstrate the computational merit of the arc-search method, the algorithm in [16] is a mimic of Mehrotra's algorithm and we have not shown its convergence 1 . The purpose of this paper is to develop some infeasible interior-point algorithms which are both computationally competitive to simplex algorithms (i.e., at least as good as Mehrotra's algorithm) and theoretically polynomial.…”

Section: Introductionmentioning

confidence: 96%

“…The proposed algorithm is very similar to Mehrotra's algorithm but replaces search direction by an arc-path suggested in [13,14]. The comprehensive numerical test for a larger pool of Netlib problems reported in [16] clearly shows the superiority of arc-search over traditional line-search method.…”

Section: Introductionmentioning

confidence: 96%

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Two computationally efficient polynomial-iteration infeasible interior-point algorithms for linear programming

Yang

2018

Numer Algor

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Linear programming has been one of the most extensively studied branches in mathematics and has been found many applications in science and engineering. Since the beginning of the development of interior-point methods, there exists a puzzling gap between the results in theory and the observations in numerical experience, i.e., algorithms with good polynomial bound are not computationally efficient and algorithms demonstrated efficiency in computation do not have a good or any polynomial bound. Todd raised a question in 2002: "Can we find a theoretically and practically efficient way to reoptimize?" This paper is an effort to close the gap. We propose two arc-search infeasible interior-point algorithms with infeasible central path neighborhood wider than all existing infeasible interior-point algorithms that are proved to be convergent. We show that the first algorithm is polynomial and its simplified version has a complexity bound equal to the best known complexity bound for all (feasible or infeasible) interior-point algorithms. We demonstrate the computational efficiency of the proposed algorithms by testing all Netlib linear programming problems in standard form and comparing the numerical results to those obtained by Mehrotra's predictor-corrector algorithm and a recently developed more efficient arc-search algorithm (the convergence of these two algorithms is unknown). We conclude that the newly proposed algorithms are not only polynomial but also computationally competitive comparing to both Mehrotra's predictor-corrector algorithm and the efficient arc-search algorithm.

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Section: Implementation Detailsmentioning

confidence: 99%

Section: Implementation Detailsmentioning

confidence: 99%

“…obtained by these two methods and select the initial point with smaller value of (72) as we guess this selection may reduce the number of iterations (see [16] for detail).…”

Section: Initial Point Selectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 96%

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Two computationally efficient polynomial-iteration infeasible interior-point algorithms for linear programming

Yang

2018

Numer Algor

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An infeasible interior-point arc-search method with Nesterov’s restarting strategy for linear programming problems

Iida,

Yamashita

2024

Comput Optim Appl

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An arc-search interior-point method is a type of interior-point method that approximates the central path by an ellipsoidal arc, and it can often reduce the number of iterations. In this work, to further reduce the number of iterations and the computation time for solving linear programming problems, we propose two arc-search interior-point methods using Nesterov’s restarting strategy which is a well-known method to accelerate the gradient method with a momentum term. The first one generates a sequence of iterations in the neighborhood, and we prove that the proposed method converges to an optimal solution and that it is a polynomial-time method. The second one incorporates the concept of the Mehrotra-type interior-point method to improve numerical performance. The numerical experiments demonstrate that the second one reduced the number of iterations and the computational time compared to existing interior-point methods due to the momentum term.

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An infeasible interior-point arc-search algorithm for nonlinear constrained optimization

2021

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CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

Cited by 13 publications

References 39 publications

Two computationally efficient polynomial-iteration infeasible interior-point algorithms for linear programming

Two computationally efficient polynomial-iteration infeasible interior-point algorithms for linear programming

An infeasible interior-point arc-search method with Nesterov’s restarting strategy for linear programming problems

An infeasible interior-point arc-search algorithm for nonlinear constrained optimization

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