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Abstract: Equations with box constraints are applied in many fields, for example the complementarity problem. After studying the existing methods, we find that quadratic convergence of majority algorithms is based on the solvability of the equations. But whether the equations are solvable is previously unknown. So, it is necessary to design an algorithm which has fast quadratic convergence. The quadratic convergence does not depend on the solvability of the equations. In this paper, we propose a new method for solving equations. The global and local quadratic convergence of the proposed algorithm are established under some suitable assumptions. We apply the proposed algorithm to a class of stochastic linear complementarity problems. Numerical results show that our method is valid. [Copyright &y& Elsevier]

Abstract: In this paper a new approach combining the features of the homotopy concept with an efficient computational algorithm which provides a simple and rigorous procedure to control the convergence of the solution is proposed to find accurate analytical explicit solutions for some oscillators with discontinuities and a fractional power restoring force which is proportional to . A very fast convergence to the exact solution was proved, since the second-order approximation lead to very accurate results. Comparisons with numerical results are presented to show the effectiveness of this method. Four numerical applications prove the accuracy of the method, which works very well for the whole range of initial amplitudes. The obtained results prove the validity and efficiency of the method, which can be easily extended to other strongly nonlinear problems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider a conic trust-region method for unconstrained optimization problems and analyze its convergence properties. We propose a convenient curvilinear search method to approximately solve the arising conic trust-region subproblem. Note that this approximate method preserves the strong convergence properties of the exact solution methods and is easy to implement. Both the linear and superlinear convergence of the method are established under commonly used conditions. Numerical experiments are conducted to show the efficiency of the new method. [Copyright &y& Elsevier]

Abstract: This paper proves the convergence of some generalized Schwarz algorithms for solvingthe obstacle problems with a T-monotone operator. Numerical results show that the generalized Schwarz algorithms converge faster than the classical Schwarz algorithms. [Copyright &y& Elsevier]