Computing a few eigenpairs of large-scale matrices is a significant problem in science and engineering applications and a very active area of research. In this paper, two methods that compute extreme eigenpairs of positive-definite matrix pencils are combined into a hybrid scheme that inherits the advantages of both constituents. The hybrid algorithm is developed and analyzed in the framework o...

Experimental measurements of angular correlations in three-jet final states have recently been performed in DIS. Next-to-leading-order QCD results for these observables are affected by large theoretical uncertainties in the kinematic region of the data. We discuss the effects of multiple QCD radiation at higher order using parton-shower methods based on transverse-momentum dependent parton dist...

We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, i.e., bilevel programs involving linear approximations of the upper-level objective and all constraintdefining functions, as well as a quadratic approximation of the lower-level objective. We describe the main features of the algorithm and the resulting software. Numerical experiments...

A trust-region-based BFGS method is proposed for solving symmetric nonlinear equations. In this given algorithm, if the trial step is unsuccessful, the linesearch technique will be used instead of repeatedly solving the subproblem of the normal trust-region method. We establish the global and superlinear convergence of the method under suitable conditions. Numerical results show that the given ...

In this paper, we present a class of trust region algorithms for minimization problems within convex feasible regions, in which the structure of the problem is explicitly used in the deenition of the trust region. This development is intended to reeect the possibility that some parts of the problem may be more accurately modelled than others, a common occurrence in large-scale nonlinear applica...

The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trust-region radius is defined by a Sobolev norm and the trust-reg...

Line search method and trust region method are two important classes of techniques for solving optimization problems and have their advantages respectively. In this paper we use the Armijo line search rule in a more accurate way and propose a new line search method for unconstrained optimization problems. Global convergence and convergence rate of the new method are analyzed under mild conditio...