Results 41 to 50 of about 244 (58)

An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean space [PDF]

arXiv, 2013
This paper is concerned with the variational inequality problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen half-space, and prove that the sequences it generates converge to the unique solution of the VIP.
arxiv  

Multi-material phase field approach to structural topology optimization [PDF]

arXiv, 2013
Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An efficient numerical method based on an $H^1$-gradient projection method is introduced and finally several ...
arxiv  

Conditional extragradient algorithms for solving variational inequalities [PDF]

arXiv, 2014
In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different linesearchs. We then establish convergence results for these algorithms under mild assumptions.
arxiv  

Stress-driven solution to rate-independent elasto-plasticity with damage at small strains and its computer implementation [PDF]

arXiv, 2015
The quasistatic rate-independent damage combined with linearized plasticity with hardening at small strains is investigated. The fractional-step time discretisation is devised with the purpose to obtain a numerically efficient scheme converging possibly to a physically relevant stress-driven solutions, which however is to be verified a-posteriori by ...
arxiv  

An extension of hybrid method without extrapolation step to equilibrium problems [PDF]

arXiv, 2015
In this paper, we introduce a new hybrid algorithm for solving equilibrium problems. The algorithm combines the extragradient method and the hybrid (outer approximation) method. In this algorithm, only an optimization program is solved at each iteration without the extra-steps like as in the extragradient method and the Armijo linesearch method.
arxiv  

A novel hybrid method for equilibrium problems and fixed point problems [PDF]

arXiv, 2015
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the extra-steps as in some previously known methods.
arxiv  

General Viscosity Implicit Midpoint Rule For Nonexpansive Mapping [PDF]

arXiv, 2016
In this work, we suggest a general viscosity implicit midpoint rule for nonexpansive mapping in the framework of Hilbert space. Further, under the certain conditions imposed on the sequence of parameters, strong convergence theorem is proved by the sequence generated by the proposed iterative scheme, which, in addition, is the unique solution of the ...
arxiv  

Rates of convergence for inexact Krasnosel'skii-Mann iterations in Banach spaces [PDF]

arXiv, 2017
We study the convergence of an inexact version of the classical Krasnosel'skii-Mann iteration for computing fixed points of nonexpansive maps. Our main result establishes a new metric bound for the fixed-point residuals, from which we derive their rate of convergence as well as the convergence of the iterates towards a fixed point.
arxiv  

Strong convergence towards the minimum norm solution via temporal scaling and Tikhonov approximation of a first-order dynamical system [PDF]

arXiv
Given a proper convex lower semicontinuous function defined on a Hilbert space and whose solution set is supposed nonempty. For attaining a global minimizer when this convex function is continuously differentiable, we approach it by a first-order continuous dynamical system with a time rescaling parameter and a Tikhonov regularization term.
arxiv  

Large volume minimizers of a non local isoperimetric problem: theoretical and numerical approaches [PDF]

arXiv, 2017
We consider the volume-constrained minimization of the sum of the perimeter and the Riesz potential. We add an external potential of the form $\|x\|^{\beta}$ that provides the existence of a minimizer for any volume constraint, and we study the geometry of big minimizers. Then we provide a numerical method to adress this variational problem.
arxiv