Abstract Adequate initial configurations for molecular dynamics simulations consist of arrangements molecules distributed in space such a way to approximately represent the system's overall structure. In order that are not disrupted by large van der Waals repulsive interactions, atoms from different must keep safe pairwise distances. Obtaining arrangement can be considered packing problem: Each type molecule satisfy spatial constraints related geometry system, and distance between greater...

Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical schemes extended to include a nonmonotone steplength strategy that is based Grippo--Lampariello--Lucidi line search. In particular, combined with spectral choice accelerate convergence process. addition nonlinear path, feasible used as search direction avoid additional trial projections during one-dimensional Convergence properties and extensive...

Augmented Lagrangian methods with general lower-level constraints are considered in the present research. These useful when efficient algorithms exist for solving subproblems which only of type. Inexact resolution constrained is considered. Global convergence proved using constant positive linear dependence constraint qualification. Conditions boundedness penalty parameters discussed. The location problems many set nonlinear addressed, employing spectral projected gradient method...

Fortran 77 software implementing the SPG method is introduced. a nonmonotone projected gradient algorithm for solving large-scale convex-constrained optimization problems. It combines classical with spectral choice of steplength and line-search strategy. The user provides objective function values, projections onto feasible set. Some recent numerical tests are reported on very large location problems, indicating that substantially more efficient than existing general-purpose problems which...

Journal Article Inexact spectral projected gradient methods on convex sets Get access Ernesto G. Birgin, Birgin Search for other works by this author on: Oxford Academic Google Scholar José Mario Martínez, Martínez Marcos Raydan IMA of Numerical Analysis, Volume 23, Issue 4, October 2003, Pages 539–559, https://doi.org/10.1093/imanum/23.4.539 Published: 01 2003

Over the last two decades, it has been observed that using gradient vector as a search direction in large-scale optimization may lead to efficient algorithms. The effectiveness relies on choosing step lengths according novel ideas are related spectrum of underlying local Hessian rather than standard decrease objective function. A review these so-called spectral projected methods for convex constrained is presented. To illustrate performance low-cost schemes, an problem set positive definite...

Optimization methods that employ the classical Powell-Hestenes-Rockafellar augmented Lagrangian are useful tools for solving nonlinear programming problems. Their reputation decreased in last 10 years due to comparative success of interior-point Newtonian algorithms, which asymptotically faster. In this research, a combination both approaches is evaluated. The idea produce competitive method, being more robust and efficient than its 'pure' counterparts critical Moreover, an additional hybrid...

This work presents the application of a recently developed numerical method to determine thickness and optical constants thin films using experimental transmittance data only. may be applied not displaying fringe pattern is shown for a-Si:H (hydrogenated amorphous silicon) layers as 100 nm. The performance limitations are discussed on basis experiments performed series six samples grown under identical conditions, but with varying from 98 nm 1.2 μm.

The focus of study in this paper is the class packing problems. More specifically, it deals with placement a set N circular items unitary radius inside an object aim minimizing its dimensions. Differently shaped containers are considered, namely circles, squares, rectangles, strips and triangles. By means resolution non-linear equations systems through Newton–Raphson method, herein presented algorithm succeeds improving accuracy previous results attained by continuous optimization approaches...

Abstract In this study, we solve the nonexact two‐stage two‐dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of patterns (nonused material or trim loss) can be used future, if they are large enough to fulfill future demands for items (ordered smaller plates). This characterized as a residual bin‐packing because possibility putting back into pieces, loss each cutting/packing pattern does not necessarily represent waste depending on its...

The evaluation complexity of general nonlinear, possibly nonconvex, constrained optimization is analyzed. It shown that, under suitable smoothness conditions, an $\epsilon$-approximate first-order critical point the problem can be computed in order $O(\epsilon^{1-2(p+1)/p})$ evaluations problem's functions and their first $p$ derivatives. This achieved by using a two-phase algorithm inspired Cartis, Gould, Toint [SIAM J. Optim., 21 (2011), pp. 1721--1739; SIAM 23 (2013), 1553--1574]. also...