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In this paper, we are concerned with the investigation problem of finding a common element of the set of fixed points of a total uniformly L-Lipschitzian mapping and the set of solutions of a system of generalized nonlinear variational-like inequalities. For this end, based on P-η-proximal mapping, an iterative algorithm is constructed and under some suitable conditions, the strong convergence and stability of the sequence generated by our proposed iterative algorithm to a common element of the above two sets are proved. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Tseng's extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The results presented in this paper generalize some known results presented in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inertial proximal point algorithm for finding a zero point of variational inclusions on Hadamard manifolds. Under suitable conditions, it is proved that the sequence generated by the algorithm converges to an element of the set of zero points of variational inclusion problem. As applications, we utilize our results to study the minimization problem and saddle point problem in the setting of Hadamard manifolds. [ABSTRACT FROM AUTHOR]

In this paper, we consider an inverse conductive scattering problem for the Helmholtz equation from measurements on the outer boundary. We want to seek reconstruction algorithms to detect the number, location, size and shape of inhomogeneities within a body. This problem is nonlinear and ill-posed, thus we should consider regularization techniques in order to improve the corresponding approximation. We examine the viability of our proposed reconstruction algorithms through the use of numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we study, from the numerical point of view, a dynamic problem involving a mixture of two viscoelastic solids. The mechanical problem is written as a system of two coupled partial differential equations. Its variational formulation is derived and an existence and uniqueness result, and an energy decay property, are recalled. Then, fully discrete approximations are introduced by using the classical finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are shown, from which we deduce the linear convergence of the algorithm. Finally, some numerical simulations, including examples in one and two dimensions, are presented to show the accuracy of the approximation and the behaviour of the solution. [ABSTRACT FROM AUTHOR]

In this paper, we construct an iterative algorithm for solving a multitime-type variational inequality problem and prove its convergence. Moreover, we study the weak sharp solutions for the multitime-type variational inequality problem and investigate the finite termination property of the constructed iterative algorithm. [ABSTRACT FROM AUTHOR]

Blind image deconvolution recovers a deblurred image and the blur kernel from a blurred image. From a mathematical point of view, this is a strongly ill-posed problem and several works have been proposed to address it. One successful approach proposed by Chan and Wong consists in using the total variation (TV) as a regularization for both the image and the kernel. These authors also introduced an Alternating Minimization (AM) algorithm in order to compute a physical solution. Unfortunately, Chan's approach suffers in particular from the ringing and staircasing effects produced by the TV regularization. To address these problems, we propose a new model based on Bilateral Total Variation (BTV) regularization of the image keeping the same regularization for the kernel. We prove the existence of a minimizer of a proposed variational problem in a suitable space using a relaxation process. We also propose an AM algorithm based on our model. The efficiency and robustness of our model are illustrated and compared with the TV method through numerical simulations. [ABSTRACT FROM AUTHOR]

A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and isotropic media. Its algorithm can be implemented very shortly and adopts to many similar partial differential equation-based eigenproblems as long as the underlying fundamental solution function can be easily generated. We develop a corroborative approximation analysis which also implicates new basic results for transmission eigenfunctions and present some numerical examples which together prove successful feasibility of our eigenvalue recovery approach. [ABSTRACT FROM AUTHOR]