Results 41 to 50 of about 243 (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  

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  

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  

A globally convergent filter-trust-region method for large deformation contact problems [PDF]

arXiv, 2017
We present a globally convergent method for the solution of frictionless large deformation contact problems for hyperelastic materials. The discretisation uses the mortar method which is known to be more stable than node-to-segment approaches. The resulting non-convex constrained minimisation problems are solved using a filter-trust-region scheme, and ...
arxiv  

Truncated Nonsmooth Newton Multigrid Methods for Block-Separable Minimization Problems [PDF]

arXiv, 2017
The Truncated Nonsmooth Newton Multigrid (TNNMG) method is a robust and efficient solution method for a wide range of block-separable convex minimization problems, typically stemming from discretizations of nonlinear and nonsmooth partial differential equations.
arxiv  

Golden ratio algorithms for solving equilibrium problems in Hilbert spaces [PDF]

arXiv, 2018
In this paper, we design a new iterative algorithm for solving pseudomonotone equilibrium problems in real Hilbert spaces. The advantage of our algorithm is that it requires only one strongly convex programming problem at each iteration. Under suitable conditions we establish the strong and weak convergence of the proposed algorithm.
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