Sharif Digital Repository

We present a non-monotone trust region algorithm for unconstrained optimization. Using the filter technique of Fletcher and Leyffer, we introduce a new filter acceptance criterion and use it to define reference iterations dynamically. In contrast with the early filter criteria, the new criterion ensures that the size of the filter is finite. We also show a correlation between problem dimension and the filter size. We prove the global convergence of the proposed algorithm to first- and second-order critical points under suitable assumptions. It is significant that the global convergence analysis does not require the common assumption of monotonicity of the sequence of objective function... 

We present a new filter trust-region approach for solving unconstrained nonlinear optimization problems making use of the filter technique introduced by Fletcher and Leyffer to generate non-monotone iterations. We also use the concept of a multidimensional filter used by Gould et al. (SIAM J. Optim. 15(1):17-38, 2004) and introduce a new filter criterion showing good properties. Moreover, we introduce a new technique for reducing the size of the filter. For the algorithm, we present two different convergence analyses. First, we show that at least one of the limit points of the sequence of the iterates is first-order critical. Second, we prove the stronger property that all the limit points... 

A novel method to compute guided mode reflectivity from optical waveguide end-facet is presented in this paper. First, rational function fitting method (RFFM) is applied in characteristic Green’s function (CGF) technique to find an approximate closed-form analytic expression for spatial Green’s function of abruptly truncated slab waveguide. Then, derived closed-form relation along with the exact results of spatial Green’s function, obtained by full wave solution, are incorporated in an efficient optimization problem. The fast Newton reflective method with trust region algorithm are utilized for optimized reflection coefficients of guided modes. The main advantage of the proposed CGF-RFFM...