We reformulate the zero-norm minimization problem as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the complementarity constraint to the objective, is exact. Then, by the special structure of the exact penalty problem, we propose a decomposition method that can seek a global optimal solution of the zero-norm minimizatio...

The limited memory BFGS (L-BFGS) method is one of the popular methods for solving large-scale unconstrained optimization. Since standard L-BFGS uses a line search to guarantee its global convergence, it sometimes requires large number function evaluations. To overcome difficulty, we propose new with certain regularization technique. We show convergence under usual assumptions. In order make mor...

Issues of surfaces, e.g., inspired from beetle's back, spider silk, cactus stem, etc., become the active area of research on designing novel materials in need of human beings to acquire fresh water resource from air. However, the design of materials on surface structure is little achieved on controlling of micro-scale drop transport in a long distance. Here, we report the ability of micro-drop ...

A modified BFGS method is proposed for unconstrained optimization. The global convergence and the superlinear convergence of the convex functions are established under suitable assumptions. Numerical results show that this method is interesting.

We present a nearly-exact method for the large scale trust region subproblem (TRS) based on the properties of the minimal-memory BFGS method. Our study in concentrated in the case where the initial BFGS matrix can be any scaled identity matrix. The proposed method is a variant of the Moré-Sorensen method that exploits the eigenstructure of the approximate Hessian B, and incorporates both the st...

In four-dimensional variational data assimilation (4D-Var) an optimal estimate of the initial state of a dynamical system is obtained by solving a large-scale unconstrained minimization problem. The gradient of the cost functional may be efficiently computed using the adjoint modeling, at the expense equivalent to a few forward model integrations; for most practical applications, the evaluation...