The power method (or iteration) is a well-known classical technique that can be used to find the dominant eigenpair of matrix. Here, we present variational quantum circuit for iteration, which eigenpairs unitary matrices and so their associated Hamiltonians. We discuss how apply combinatorial optimization problems formulated as quadratic unconstrained binary its complexity. In addition, run num...

In this Letter, we study Kaup-Boussinesq system by using the wellknown He’s variational approach. In fact, the He’s variational method is a promising method to various systems of linear and nonlinear equations.

In this paper, we suggest and analyze a new three-step iterative algorithm for solving the general variational inequalities. We also study the global convergence of the proposed method under some mild conditions. Since the general variational inequalities include variational inequalities, quasi variational inequalities and quasi complementarity problems as special cases, one can deduce similar ...

We introduce and discuss the Homotopy perturbation method, the Adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. Then, we give an example of the stefan problem with  kinetics and solve it by these methods.

In this paper, we first introduce a monotone mapping and its resolvent in general metric spaces.Then, we give two new iterative methods  by combining the resolvent method with Halpern's iterative method and viscosity approximation method for  finding a fixed point of monotone mappings and a solution of variational inequalities. We prove convergence theorems of the proposed iterations  in ...

Many computationally-efficient methods for Bayesian deep learning rely on continuous optimization algorithms, but the implementation of these methods requires significant changes to existing code-bases. In this paper, we propose Vprop, a method for Gaussian variational inference that can be implemented with two minor changes to the off-the-shelf RMSprop optimizer. Vprop also reduces the memory ...

Modifying von Neumann’s alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly con…ne our attention to the two-set CSVIP, which entails …nding common solutions to two unrelated variational inequalities in Hilbert space. Keywords: Alternating method, averaged op...

In this work, we are going to obtain approximate solutions for Lie ́nard equations using He's variational iteration method. This method proves to be very promising for obtaining approximate solutions for this kind of equations. We also demonstrate the superiority of variational iteration method over the decomposition method for this type of equations providing numerical comparisons.

We present a novel variational formulation of discrete deformable registration as the minimization of a convex energy functional that involves diffusion regularization. We show that a finite difference solution (FD) of the variational formulation is equivalent to a continuous-valued Gaussian Markov random field (MRF) energy minimization formulation previously proposed as the random walker defor...

Since the fundamental theory of variational inequality was founded in the 1960s, the variational inequality theory with applications has made powerful progress and has become an important part of nonlinear analysis. It has been applied intensively to mechanics, differential equation, cybernetics, quantitative economics, optimization theory, nonlinear programming, and so forth (see [2]). In virt...