Search

Aiming at the phenomenon of slow convergence rate and low accuracy of bat algorithm, a novel bat algorithm based on differential operator and Lévy lights trajectory is proposed. In this paper, a differential operator is introduced to accelerate the convergence speed of proposed algorithm, which is similar to mutation strategy "DE/best/2" in differential algorithm. Lévy lights trajectory can ensure the diversity of the population against premature convergence and make the algorithm effectively jump out of local minima. 14 typical benchmark functions and an instance of nonlinear equations are tested; the simulation results not only show that the proposed algorithm is feasible and effective, but also demonstrate that this proposed algorithm has superior approximation capabilities in high-dimensional space. [ABSTRACT FROM AUTHOR]

Under the condition that the values of mapping F are evaluated approximately, we propose a proximal analytic center cutting plane algorithm for solving variational inequalities. It can be considered as an approximation of the earlier cutting plane method, and the conditions we impose on the corresponding mappings are more relaxed. The convergence analysis for the proposed algorithm is also given at the end of this paper. [ABSTRACT FROM AUTHOR]

Very recently, Ahmad and Yao 2009( introduced and considered a system of generalized resolvent equationswith corresponding system of variational inclusions in uniformly smooth Banach spaces. In this paper we introduce and study a general system of generalized resolvent equations with corresponding general system of variational inclusions in uniformly smooth Banach spaces. We establish an equivalence relation between general system of generalized resolvent equations and general system of variational inclusions. The iterative algorithms for finding the approximate solutions of general system of generalized resolvent equations are proposed. The convergence criteria of approximate solutions of general system of generalized resolvent equations obtained by the proposed iterative algorithm are also presented. Our results represent the generalization, improvement, supplement, and development of Ahmad and Yao corresponding ones. [ABSTRACT FROM AUTHOR]

Very recently, Moudafi (2011) introduced an algorithm with weak convergence for the split common fixed-point problem. In this paper, we will continue to consider the split common fixedpoint problem. We discuss the strong convergence of the viscosity approximation method for solving the split common fixed-point problem for the class of quasi-nonexpansive mappings in Hilbert spaces. Our results improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a nonlinear stationary Stokes problem with mixed boundary conditions that describes the ice velocity and pressure fields of grounded glaciers under Glen's flow law. Using convex analysis arguments, we prove the existence and the uniqueness of a weak solution. A finite element method is applied with approximation spaces that satisfy the inf-sup condition, and a priori error estimates are established by using a quasinorm technique. Several algorithms including Newton's method are proposed to solve the nonlinearity of the Stokes problem and are proved to be convergent. Our results are supported by numerical convergence studies. [ABSTRACT FROM AUTHOR]

The minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming algorithms. When the number of variables is large, one of the most widely used strategies is to project the original problem into a small dimensional subspace. In this paper, we introduce an algorithm for solving nonlinear least squares problems. This algorithm is based on constructing a basis for the Krylov subspace in conjunction with a model trust region technique to choose the step. The computational step on the small dimensional subspace lies inside the trust region. The Krylov subspace is terminated such that the termination condition allows the gradient to be decreased on it. A convergence theory of this algorithm is presented. It is shown that this algorithm is globally convergent. [ABSTRACT FROM AUTHOR]