CONVERGENCE ANALYSIS OF A PROXIMAL POINT ALGORITHM FOR MINIMIZING DIFFERENCES OF FUNCTIONS

... 3.6 For a suitable choice of the mappings A, η, F, M, Ik , and space X, then the Algorithm 3.5 can be degenerated to the hybrid proximal point algorithm 16, 17 and the over-relaxed A-proximal point ... generalized version of the over-relaxed proximal point algorithm and its applications to approximation solvability of the inclusion problem of the form 2.1 b...

Ngày tải lên: 21/06/2014, 05:20

... Muglia, and Y Yao, “On a two-step algorithm for hierarchical fixed point problems and variational inequalities,” Journal of Inequalities and Applications, vol 2009, Article ID 208692, 13 pages, ... Fix T such that Ax, x − x ≥ 0, ∀x ∈ Fix T , 1.7 a variational inequality studied by Yamada and Ogura 10 A Example 1.3 Let A be a maximal monotone operator Taking...

Ngày tải lên: 21/06/2014, 07:20

... 2010, Article ID 383740, 19 pages, 2010 11 P Cholamjiak and S Suantai, A new hybrid algorithm for variational inclusions, generalized equilibrium problems, and a finite family of quasi -nonexpansive ... P Katchang and P Kumam, A general iterative method of fixed points for mixed equilibrium problems and variational inclusion problems, Journal of...

Ngày tải lên: 21/06/2014, 07:20

... Unfortunately, a small value of the step size will make the algorithm converge very slowly, and a large value of the controlling parameter will make the LMS algorithm essentially dominant The rest of ... “Performance analysis of the lp norm back propagation algorithm for adaptive equalisation,” IEE Proceedings, Part F: Radar and Signal Processing, vol 140, no 1, pp 43–47, 1993...

Ngày tải lên: 21/06/2014, 08:20

... delays through fixed point theory, ” Fixed Point Theory and Applications, vol 2008, Article ID 480187, 20 pages, 2008 13 A T M Lau, H Miyake, and W Takahashi, “Approximation of fixed points for amenable ... iteration for nonexpansive mappings,” Fixed Point Theory and Applications, vol 2008, Article ID 649162, pages, 2008 Y Qing and B E Rhoades, “T -stability of...

Ngày tải lên: 21/06/2014, 20:20

... Fixed Point Theory and Applications more general Banach spaces; see Kamimura and Takahashi and Ohsawa and Takahashi In 2004, Kamimura et al considered the algorithm 1.2 in a uniformly smooth and ... of a maximal monotone operator and the solution set of the variational inequality problem for an inverse- strongly- monotone operator in a 2-uniformly convex and unifor...

Ngày tải lên: 21/06/2014, 20:20

... of two variational inequalities VI C ,A and VI C,B PC ; solution of a system of two mixed equilibrium problems Tn Trn and Vn solution of a mixed equilibrium problem and a variational inequality ... prove a strong convergence theorem to approximate a fixed point of S that is also a solution of a mixed equilibrium problem and a solution...

Ngày tải lên: 21/06/2014, 20:20

... PΩ x − PΩ y for all x, y ∈ H, iv xn → x0 weakly and P xn → y0 strongly imply that P x0 y0 Finding zeroes of maximal monotone operators is the central and important topic in nonlinear functional ... following set-valued equation: ∈ T z, 1.5 where T : Ω → 2H is a maximal monotone operator, is the proximal point algorithm which, starting with any point x0 ∈ H, updates x...

Ngày tải lên: 22/06/2014, 06:20

... Journal of Mathematical Analysis and Applications, vol 279, no 2, pp 372– 379, 2003 G Bigi, M Castellani, and G Kassay, A dual view of equilibrium problems, Journal of Mathematical Analysis and ... Theory and Applications 32 W Nilsrakoo and S Saejung, “Strong convergence theorems for a countable family of quasiLipschitzian mappings and its applications,” Journal...

Ngày tải lên: 22/06/2014, 11:20

... “The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming,” Mathematical Programming, 2008 D Noll, “Local convergence of an augmented Lagrangian method for ... Optimality conditions Let the Lagrangian function of 1.1 be L x, λ, μ f x λ, h x μ, g x 2.8 Journal of Inequalities and Applications Robinson’s constraint qualification...

Ngày tải lên: 22/06/2014, 18:20

... PΩ x − PΩ y for all x, y ∈ H, iv xn → x0 weakly and P xn → y0 strongly imply that P x0 y0 Finding zeroes of maximal monotone operators is the central and important topic in nonlinear functional ... following set-valued equation: ∈ T z, 1.5 where T : Ω → 2H is a maximal monotone operator, is the proximal point algorithm which, starting with any point x0 ∈ H, updates x...

Ngày tải lên: 22/06/2014, 18:20

... spaces Kazmi and Bhat [34] introduced a system of nonlinear variational- like inclusions and gave an iterative algorithm for finding its approximate solution Fang and Huang [35] and Fang et al ... of Inequalities and Applications [11] S Adly, “Perturbed algorithms and sensitivity analysis for a general class of variational inclusions, ” Journal of Mathem...

Ngày tải lên: 22/06/2014, 19:20

... existence of an inverse mapping for a given nonlinear expanding mapping of X into itself involves a specific fixed point theorem As a corollary of our main Theorem 5.1, we obtain the following fixed point ... [5] V Azhmyakov, Stable Operators in Analysis and Optimization, Peter Lang, Berlin, 2005 [6] C Baiocchi and A Capelo, Variational and Quasivariational Inequali...

Ngày tải lên: 22/06/2014, 22:20

... Predictor-Corrector Algorithm General Theory for Asymptotic Analyticity of Off-Central Path for SDLCP Analysis of Off-Central Paths for SOCP 36 63 3.1 Off-Central Path for SOCP ... related to the local convergence behaviour of path- following interior point algorithm [26, 22] In Chapter 2, we consider off-central path for SDLCP We show the existen...

Ngày tải lên: 16/09/2015, 17:11

... property at each point of dom ∂ C f A Generalized Proximal Point Algorithm for Minimizing Differences of Functions We focus on the convergence analysis of a proximal point algorithm for solving ... variational analysis in analyzing nonsmooth optimization algorithms, we introduce and study convergence analysis of a proximal point algorithm...

Ngày tải lên: 12/10/2015, 16:21