An extension of the auxiliary problem principle to nonsymmetric auxiliary operators
A. Renaud, G. Cohen (1997)
ESAIM: Control, Optimisation and Calculus of Variations
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A. Renaud, G. Cohen (1997)
ESAIM: Control, Optimisation and Calculus of Variations
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Alexandre, P. (1999)
Serdica Mathematical Journal
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We work on the research of a zero of a maximal monotone operator on a real Hilbert space. Following the recent progress made in the context of the proximal point algorithm devoted to this problem, we introduce simultaneously a variable metric and a kind of relaxation in the perturbed Tikhonov’s algorithm studied by P. Tossings. So, we are led to work in the context of the variational convergence theory.
Pang, Li-Ping, Xia, Zun-Quan (2003)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 90C25, 68W10, 49M37. A general framework of the (parallel variable transformation) PVT-type algorithm, called the PVT-MYR algorithm, for minimizing a non-smooth convex function is proposed, via the Moreau-Yosida regularization. As a particular scheme of this framework an ε-scheme is also presented. The global convergence of this algorithm is given under the assumptions of strong convexity of the objective function and an ε-descent...
A. Renaud, G. Cohen (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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To find a zero of a maximal monotone operator, an extension of the Auxiliary Problem Principle to nonsymmetric auxiliary operators is proposed. The main convergence result supposes a relationship between the main operator and the nonsymmetric component of the auxiliary operator. When applied to the particular case of convex-concave functions, this result implies the convergence of the parallel version of the Arrow-Hurwicz algorithm under the assumptions of Lipschitz and partial...
Lulu Yin, Hongwei Liu, Jun Yang (2022)
Applications of Mathematics
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We propose a modification of the golden ratio algorithm for solving pseudomonotone equilibrium problems with a Lipschitz-type condition in Hilbert spaces. A new non-monotone stepsize rule is used in the method. Without such an additional condition, the theorem of weak convergence is proved. Furthermore, with strongly pseudomonotone condition, the $R$-linear convergence rate of the method is established. The results obtained are applied to a variational inequality problem, and the convergence...
Aleksandr N. Antamoshkin, V. N. Saraev, Evgeniĭ Semënkin (1990)
Kybernetika
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Chiriac, Corina L. (2004)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Goran Lešaja (2002)
The Yugoslav Journal of Operations Research
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Alber, Y.I., Burachik, R.S., Iusem, A.N. (1997)
Abstract and Applied Analysis
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