In this paper, a monotone linear complementarity reformulation of the nonnegative least squares problems in inequality sense is introduced. Then Mehrotra’s predictor-corrector interior point algorithm is applied to solve the resulting monotone linear complementarity problem. Our numerical experiments on several randomly generated test problems show that Mehrotra’s algorithm overperforms the wid...

In this paper we prove that the Newton method applied to the generalized equation y ∈ f(x) + F (x) with a C function f and a set-valued map F acting in Banach spaces, is locally convergent uniformly in the parameter y if and only if the map (f +F ) is Aubin continuous at the reference point. We also show that the Aubin continuity actually implies uniform Q-quadratic convergence provided that th...

The q-generalizations of the two fundamental statements of matrix algebra – the Cayley-Hamilton theorem and the Newton relations – to the cases of quantum matrix algebras of an ”RTT-” and of a ”Reflection equation” types have been obtained in [2]–[6]. We construct a family of matrix identities which we call Cayley-HamiltonNewton identities and which underlie the characteristic identity as well ...

We study local convergence of generalized Newton methods for both equations and inclusions by using known and new approximations and regularity properties at the solution. Including Kantorovich-type settings, our goal are statements about all (not only some) Newton sequences with appropriate initial points. Our basic tools are results of [31], [37] and [40], mainly about Newton maps and modifie...

We design a well-developed algorithm for solving large bound-constrained systems. The method combines a subspace trust-region strategy with a Newton-Krylov method and with a strategy for handling the bounds. To solve the trust-region problem efficiently, we look for an approximate solution and do not require the exact solution of the Newton equation. In addition, a strategy for obtaining an imp...

In this paper, the numerical design of a Nash equilibrium for infinite horizon multiparameter singularly perturbed systems (MSPS) is analyzed. A new algorithm which is based on the Newton’s method for solving the generalized cross–coupled multiparameter algebraic Riccati equations (GCMARE) is proposed. It is proven that the proposed algorithm guarantees the quadratic convergence. As a result, i...

Robust and efficient solution techniques for solving macroeconometric models are increasingly becoming a key factor in developing models employed by policy-making institutions for policy simulations and forecasting. Traditionally, when solved in presence of forward-looking variables, these models are nonlinear, large-scale and sparse and give rise to large and highly structured nonlinear system...

When an airfoil is pitched up rapidly, a dynamic stall vortex forms at the leading edge and produces high transient lift before shedding and stall occur. The aim of this work is to develop low-dimensional models of the dynamics of these leading-edge vortices, which may be used to develop feedback laws to stabilize these vortices using closed-loop control, and maintain high lift. We first perfor...