An Efficient Neural Network Model for Solving the Absolute Value Equations

Mansoori, Amin; Eshaghnezhad, Mohammad; Effati, Sohrab

doi:10.1109/tcsii.2017.2750065

Cited by 33 publications

(10 citation statements)

References 19 publications

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“…There are diverse neural solutions to various types of optimizing problems; linear [29] and nonlinear [13], smooth [32] and non-smooth [27], and so on. Recently, a novel neural network is proposed to solve the absolute value equation (APV) [19]. The neural network is guaranteed to converge to the exact solution of the APV.…”

Section: Introductionmentioning

confidence: 99%

A novel one-layer recurrent neural network for the l1-regularized least square problem

Mohammadi

Tan

Hofman³

et al. 2018

Neurocomputing

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The l1 regularized least square problem, or the lasso, is a non-smooth convex minimization which is widelyused in diverse fields. However, solving such a minimization is not straightforward since it is not differentiable. In this paper, an equivalent smooth minimization with box constraints is obtained, and it is proved to be equivalent to the lasso problem. Accordingly, an efficient recurrent neural network is developed which guarantees to globally converge to the solution of the lasso. Further, it is investigated that the property "the dual of dual is primal" holds for the l1 regularized least square problem. The experiments on image and signal recovery illustrate the reasonable performance of the proposed neural network.Index Terms-sparse, l1 regularization, smooth, neural network.

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Section: Introductionmentioning

confidence: 99%

A novel one-layer recurrent neural network for the l1-regularized least square problem

Mohammadi

Tan

Hofman³

et al. 2018

Neurocomputing

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“…By the help of Proposition (16) with Theorems ( 11), ( 12) and ( 13), we obtained the following results, see Theorem (17), Theorem (18) and Theorem (19) respectively.…”

Section: Resultsmentioning

confidence: 90%

“…The study of the absolute value equations is going in two directions: one is a theoretical analysis of AVEs (see [2,4,7,8,9,10] and references therein). Another one is, based on theoretical analysis to develop some numerical methods (see [11,12,13,14,15,16,17,18,19] and references therein), for the solution of AVEs. Solving and checking the unique solution of the AVEs is an NP-hard problem [3].…”

Section: Introductionmentioning

confidence: 99%

The unique solvability conditions for a new class of absolute value equation

Kumar

Deepmala

2023

YUGOSLAV J OPERATION

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In this article, we investigate the solution of a new class of the absolute value equation (NCAVE) A1x ? |B1x ? c| = d. Based on spectral radius condition, singular value condition and row and column W-property, some necessary and sufficient conditions for unique solvability for NCAVE are gained. Some new results for the unique solvability of the new generalized absolute value equation (NGAVE) A1x?|B1x| = d are also obtained.

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“…The dynamical system (1.6) can be traced back to [3,9,13,29]. Under certain conditions, the above mentioned dynamical systems are globally asymptotically stable [2,17,18,31]. However, in practice, the finite-time convergence proposed in [1] is more attractive than the classical asymptotic stability over infinite time [11].…”

Section: Introductionmentioning

confidence: 99%

A New Fixed-Time Dynamical System for Absolute Value Equations

Li¹,

Yu²,

Yang³

et al. 2023

NMTMA

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A novel dynamical model with fixed-time convergence is presented to solve the system of absolute value equations (AVEs). Under a mild condition, it is proved that the solution of the proposed dynamical system converges to the solution of the AVEs. Moreover, in contrast to the existing inversion-free dynamical system (C. Chen et al., Appl. Numer. Math. 168 (2021), 170-181), a conservative settling-time of the proposed method is given. Numerical simulations illustrate the effectiveness of the new method.

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An Efficient Neural Network Model for Solving the Absolute Value Equations

Cited by 33 publications

References 19 publications

A novel one-layer recurrent neural network for the l1-regularized least square problem

A novel one-layer recurrent neural network for the l1-regularized least square problem

The unique solvability conditions for a new class of absolute value equation

A New Fixed-Time Dynamical System for Absolute Value Equations

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