In this paper, we propose a retrospective filter trust region algorithm for unconstrained optimization, which is based on the framework of the retrospective trust region method and associated with the technique of the multi-dimensional filter. The new algorithm gives a good estimation of trust region radius, relaxes the condition of accepting a trial step for the usual trust region methods. Und...

We present a novel methodology that utilizes four-dimensional (4D) space deformation to simulate a magnification lens on versatile volume datasets and textured solid models. Compared with other magnification methods (e.g. geometric optics, mesh editing), 4D differential geometry theory and its practices are much more flexible and powerful for preserving shape features (i.e. minimizing angle dis...

Solving the trust-region subproblem (TRS) plays a key role in numerical optimization and many other applications. The generalized Lanczos (GLTR) method is well-known type approach for solving large-scale TRS. projects original TRS onto sequence of lower dimensional Krylov subspaces, whose orthonormal bases are generated by symmetric process, computes approximate solutions from underlying subspa...

and Applied Analysis 3 2.3. The Improved Accepted Condition for d k . Borrowed from the usual trust region idea, we also need to define the following predicted reduction for the violation function h(x) = ‖c(x)‖ 2 predc k = h (x k ) − 󵄩󵄩󵄩󵄩 c k + A T