A dynamic model to solve the absolute value equations

Mansoori, Amin; Erfanian, Majid

doi:10.1016/j.cam.2017.09.032

Cited by 57 publications

(14 citation statements)

References 25 publications

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“…where B ∈ R n×n was introduced by Rohn [32] and investigated in [23]. The AVEs have received much attention because they are used as a useful tool in the optimization field, such as the linear and quadratic programming, the optimal stopping in Markov chain, the structural mechanics, the network prices, the network equilibrium problems, the journal bearings, and the contact problems; see [3,8,16,17,24,27,35,36,38] and the references therein.…”

Section: Consider the Absolute Value Equation (Ave) With Matrixmentioning

confidence: 99%

Iterative methods for solving absolute value equations

Ali¹,

Ali²,

Iqbal³

2021

J. Math. Computer Sci.

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We suggest and analyze some iterative methods called Jacobi, Gauss-Seidel, SOR (successive over-relaxation), and modified Picard methods for solving absolute value equations Ax − |x| = b, where A is an M-matrix, b ∈ R n is a real vector, and x ∈ R n is unknown. Furthermore, we discuss the convergence of the suggested methods under suitable assumptions and represent their performance through our numerical results. Results are very encouraging and may stimulate further research in this direction.

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Section: Consider the Absolute Value Equation (Ave) With Matrixmentioning

confidence: 99%

Iterative methods for solving absolute value equations

Ali¹,

Ali²,

Iqbal³

2021

J. Math. Computer Sci.

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“…The pioneering works on an RNN model for optimization were done by Hopfield and Tank [15]. Neurodynamic optimization has received great success in recent years; see [8][9][10][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Assignment model with multi-objective linear programming for allocating choice ranking using recurrent neural network

2021

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Classic linear assignment method is a multi-criteria decision-making approach in which criteria are weighted and each rank is assigned to a choice. In this study, to abandon the requirement of calculating the weight of criteria and use decision attributes prioritizing and also to be able to assign a rank to more than one choice, a multi-objective linear programming (MOLP) method is suggested. The objective function of MOLP is defined for each attribute and MOLP is solved based on absolute priority and comprehensive criteria methods. For solving the linear programming problems we apply a recurrent neural network (RNN). Indeed, the Lyapunov stability of the model is proved. Results of comparing the proposed method with TOPSIS, VICOR, and MOORA methods which are the most common multi-criteria decision schemes show that the proposed approach is more compatible with these methods.

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“…Hu et al proposed a generalized Newton method for absolute value equations associated with second order cones (SOCAVE), which is an extension of GAVE (1.1) [15]. For more numerical algorithms, one can refer to [1,4,8,10,17,25,46] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A non-monotone smoothing Newton algorithm for solving the system of generalized absolute value equations

Chen

Yu²,

Han

et al. 2021

Preprint

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The system of generalized absolute value equations (GAVE) has attracted more and more attention in the optimization community. In this paper, by introducing a smoothing function, we develop a smoothing Newton algorithm with non-monotone line search to solve the GAVE. We show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the GAVE. Numerical results are given to demonstrate the viability and efficiency of the approach.

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A dynamic model to solve the absolute value equations

Cited by 57 publications

References 25 publications

Iterative methods for solving absolute value equations

Iterative methods for solving absolute value equations

Assignment model with multi-objective linear programming for allocating choice ranking using recurrent neural network

A non-monotone smoothing Newton algorithm for solving the system of generalized absolute value equations

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