Economic and social activity is increasingly reflected in operations on digital objects and network-mediated interactions between digital entities. Trust is a prerequisite for many of these interactions, particularly if items of value are to be exchanged. In this paper the probabilistic model and computational approaches found in some network reliability models are applied to modelling computat...

In this paper, we incorporate a nonmonotone technique with the new proposed adaptive trust region radius (Shi and Guo, 2008) [4] in order to propose a new nonmonotone trust region method with an adaptive radius for unconstrained optimization. Both the nonmonotone techniques and adaptive trust region radius strategies can improve the trust region methods in the sense of global convergence. The g...

In this paper we consider the regularity of the trust region-cg algorithm, when it is applied to nonlinear ill-posed iverse problems. The trust region algorithm can be viewed as a regularization method, but it diiers from the traditional regularization method, because no penalty term is need. Thus, the determing of the so-called regular-ization parameter in a standard regularization method is a...

In this paper, we present a new trust region method for nonlinear equations with the trust region converging to zero. The new method preserves the global convergence of the traditional trust region methods in which the trust region radius will be larger than a positive constant. We study the convergence rate of the new method under the local error bound condition which is weaker than the nonsin...

This paper presents a simple but eecient way to nd a good initial trust region radius in trust region methods for nonlinear optimization. The method consists of monitoring the agreement between the model and the objective function along the steepest descent direction, computed at the starting point. Further improvements for the starting point are also derived from the information gleaned during...

In this paper, we present a new trust region method for unconstrained nonlinear programming in which we blend adaptive trust region algorithm by non-monotone strategy to propose a new non-monotone trust region algorithm with automatically adjusted radius. Both non-monotone strategy and adaptive technique can help us introduce a new algorithm that reduces the number of iterations and function ev...

In (NAR 08/18 and 08/21, Oxford University Computing Laboratory, 2008) we introduced a second-derivative SQP method (S2QP) for solving nonlinear nonconvex optimization problems. We proved that the method is globally convergent and locally superlinearly convergent under standard assumptions. A critical component of the algorithm is the so-called predictor step, which is computed from a strictly ...

In a recent paper, Dennis, El{Alem, and Maciel proved global convergence to a stationary point for a general trust{region{based algorithm for equality{constrained optimization. This general algorithm is based on appropriate choices of trust{region subproblems and seems particularly suitable for large problems. This paper shows global convergence to a point satisfying the second{order necessary ...

A nonmonotone trust-region method for the solution of nonlinear systems of equations with box constraints is considered. The method differs from existing trust-region methods both in using a new nonmonotonicity strategy in order to accept the current step and by using a new updating technique for the trust-region-radius. The overall method is shown to be globally convergent. Moreover, when comb...

We propose a trust region algorithm for solving nonconvex smooth optimization problems that, in the worst case, is able to drive the norm of the gradient of the objective function below a prescribed threshold of > 0 after at most O( −3/2) iterations, function evaluations, and derivative evaluations. This improves upon the O( −2) bound known to hold for some other trust region algorithms and mat...