1978
DOI: 10.1051/m2an/1978120201531
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Perturbation des méthodes d'optimisation. Applications

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Cited by 54 publications
(28 citation statements)
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“…Let Θ(x, y) = 0 for all x, y ∈ C , S n = I for all n ∈ N, γ ≡ 1, B ≡ I and f := x in Theorem 3.1, then MEP(Θ, ϕ) = Argmin(ϕ). It follows from Theorem 3.1 that the iterative sequence {x n } defined by          x 1 = x ∈ C chosen arbitrarily, u n = argmin y∈C ϕ(y) + 1 2r n y − x n 2 , y n = P C (u n − λ n Au n ), x n+1 = α n x + β n x n + (1 − β n − α n )P C (u n − λ n Ay n ), ∀n ≥ 1, x n+1 = α n x + β n x n + (1 − β n − α n )u n , ∀n ≥ 1, We remark that the algorithms (3.37) and (3.38) are variants of the proximal method for optimization problems introduced and studied by Martinet [44], Rockafellar [45], Ferris [46] and many others.…”
Section: Resultsmentioning
confidence: 99%
“…Let Θ(x, y) = 0 for all x, y ∈ C , S n = I for all n ∈ N, γ ≡ 1, B ≡ I and f := x in Theorem 3.1, then MEP(Θ, ϕ) = Argmin(ϕ). It follows from Theorem 3.1 that the iterative sequence {x n } defined by          x 1 = x ∈ C chosen arbitrarily, u n = argmin y∈C ϕ(y) + 1 2r n y − x n 2 , y n = P C (u n − λ n Au n ), x n+1 = α n x + β n x n + (1 − β n − α n )P C (u n − λ n Ay n ), ∀n ≥ 1, x n+1 = α n x + β n x n + (1 − β n − α n )u n , ∀n ≥ 1, We remark that the algorithms (3.37) and (3.38) are variants of the proximal method for optimization problems introduced and studied by Martinet [44], Rockafellar [45], Ferris [46] and many others.…”
Section: Resultsmentioning
confidence: 99%
“…Sua invençãoé atribuída a Martinet [6], cujas ideias foram amplamente desenvolvidas por Rockafellar [12]. Embasados em [5,13], o método clássico de ponto proximal consiste em minimizar uma função f : R n → R convexa por meio de uma sequência x k gerada conforme (1):…”
Section: Introductionunclassified
“…The proximal point algorithm (PPA) is known for its theoretically nice convergence properties, which was first proposed by Martinet [16] and further studied by Rockafellar [24]. PPA is a procedure for finding a vector z satisfying 0 ∈ T (z), where T is a maximal monotone operator.…”
Section: Introductionmentioning
confidence: 99%