2018
DOI: 10.1016/j.cam.2017.06.019
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Solving absolute value equation using complementarity and smoothing functions

Abstract: In this paper, we reformulate the NP-hard problem of the absolute value equation (AVE) as a horizontal linear complementarity one and then solve it using a smoothing technique. This approach leads to a new class of methods that are valid for general absolute value equation. An asymptotic analysis proves the convergence of our schemes and provides some interesting error estimates. This kind of error bound or estimate had never been studied for other known methods. The corresponding algorithms were tested on ran… Show more

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Cited by 58 publications
(53 citation statements)
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“…The point x * = (1, 1) T satisfies ∇Θ(x * , F (x * )) = 0 and therefore is a stationary point of (P). However, this point is not a solution of (1).…”
Section: Sufficient Optimality Condition For the Montone Ncpmentioning
confidence: 96%
See 4 more Smart Citations
“…The point x * = (1, 1) T satisfies ∇Θ(x * , F (x * )) = 0 and therefore is a stationary point of (P). However, this point is not a solution of (1).…”
Section: Sufficient Optimality Condition For the Montone Ncpmentioning
confidence: 96%
“…For r sufficiently small, the functions θ approximate a step function. This observation already leads to interesting results in sparse optimization in [19] and applied in the context of complementarity problems in [1,13]. We use the function Θ to reformulate the NCP as follows…”
Section: A New Merit Function For Complementarity Problemsmentioning
confidence: 99%
See 3 more Smart Citations