Exploiting damped techniques for nonlinear conjugate gradient methods

In this paper we propose the use of damped techniques within Nonlinear Conjugate Gradient (NCG) methods. Damped techniques were introduced by Powell and recently reproposed by Al-Baali and till now, only applied in the framework of quasi–Newton methods. We extend their use to NCG methods in large scale unconstrained optimization, aiming at possibly improving the efficiency and the robustness of the latter methods, especially when solving difficult problems. We consider both unpreconditioned and Preconditioned NCG (PNCG). In the latter case, we embed damped techniques within a class of preconditioners based on quasi–Newton updates. Our purpose is to possibly provide efficient preconditioners which approximate, in some sense, the inverse of the Hessian matrix, while still preserving information provided by the secant equation or some of its modifications. The results of an extensive numerical experience highlights that the proposed approach is quite promising

Filter-based stochastic algorithm for global optimization

We propose the general Filter-based Stochastic Algorithm (FbSA) for the global optimization of nonconvex and nonsmooth constrained problems. Under certain conditions on the probability distributions that generate the sample points, almost sure convergence is proved. In order to optimize problems with computationally expensive black-box objective functions, we develop the FbSA-RBF algorithm based on the general FbSA and assisted by Radial Basis Function (RBF) surrogate models to approximate the objective function. At each iteration, the resulting algorithm constructs/updates a surrogate model of the objective function and generates trial points using a dynamic coordinate search strategy similar to the one used in the Dynamically Dimensioned Search method. To identify a promising best trial point, a non-dominance concept based on the values of the surrogate model and the constraint violation at the trial points is used. Theoretical results concerning the sufficient conditions for the almost surely convergence of the algorithm are presented. Preliminary numerical experiments show that the FbSA-RBF is competitive when compared with other known methods in the literature.The authors are grateful to the anonymous referees for their fruitful comments and suggestions.The first and second authors were partially supported by Brazilian Funds through CAPES andCNPq by Grants PDSE 99999.009400/2014-01 and 309303/2017-6. The research of the thirdand fourth authors were partially financed by Portuguese Funds through FCT (Fundação para Ciência e Tecnologia) within the Projects UIDB/00013/2020 and UIDP/00013/2020 of CMAT-UM and UIDB/00319/2020

Quasi-Newton-Based Preconditioning and Damped Quasi-Newton Schemes for Nonlinear Conjugate Gradient Methods

In this paper, we deal with matrix-free preconditioners for Nonlinear Conjugate Gradient (NCG) methods. In particular, we review proposals based on quasi-Newton updates, and either satisfying the secant equation or a secant-like equation at some of the previous iterates. Conditions are given proving that, in some sense, the proposed preconditioners also approximate the inverse of the Hessian matrix. In particular, the structure of the preconditioners depends both on low-rank updates along with some specific parameters. The low-rank updates are obtained as by-product of NCG iterations. Moreover, we consider the possibility to embed damped techniques within a class of preconditioners based on quasi-Newton updates. Damped methods have proved to be effective to enhance the performance of quasi-Newton updates, in those cases where the Wolfe linesearch conditions are hardly fulfilled. The purpose is to extend the idea behind damped methods also to improve NCG schemes, following a novel line of research in the literature. The results, which summarize an extended numerical experience using large-scale CUTEst problems, is reported, showing that these approaches can considerably improve the performance of NCG methods

In silico modeling of the specific inhibitory potential of thiophene-2,3-dihydro-1,5-benzothiazepine against BChE in the formation of β-amyloid plaques associated with Alzheimer's disease

<p>Abstract</p> <p>Background</p> <p>Alzheimer's disease, known to be associated with the gradual loss of memory, is characterized by low concentration of acetylcholine in the hippocampus and cortex part of the brain. Inhibition of acetylcholinesterase has successfully been used as a drug target to treat Alzheimer's disease but drug resistance shown by butyrylcholinesterase remains a matter of concern in treating Alzheimer's disease. Apart from the many other reasons for Alzheimer's disease, its association with the genesis of fibrils by β-amyloid plaques is closely related to the increased activity of butyrylcholinesterase. Although few data are available on the inhibition of butyrylcholinesterase, studies have shown that that butyrylcholinesterase is a genetically validated drug target and its selective inhibition reduces the formation of β-amyloid plaques.</p> <p>Rationale</p> <p>We previously reported the inhibition of cholinesterases by 2,3-dihydro-1, 5-benzothiazepines, and considered this class of compounds as promising inhibitors for the cure of Alzheimer's disease. One compound from the same series, when substituted with a hydroxy group at C-3 in ring A and 2-thienyl moiety as ring B, showed greater activity against butyrylcholinesterase than to acetylcholinesterase. To provide insight into the binding mode of this compound (Compound A), molecular docking in combination with molecular dynamics simulation of 5000 ps in an explicit solvent system was carried out for both cholinesterases.</p> <p>Conclusion</p> <p>Molecular docking studies revealed that the potential of Compound A to inhibit cholinesterases was attributable to the cumulative effects of strong hydrogen bonds, cationic-π, π-π interactions and hydrophobic interactions. A comparison of the docking results of Compound A against both cholinesterases showed that amino acid residues in different sub-sites were engaged to stabilize the docked complex. The relatively high affinity of Compound A for butyrylcholinesterase was due to the additional hydrophobic interaction between the 2-thiophene moiety of Compound A and Ile69. The involvement of one catalytic triad residue (His438) of butyrylcholinesterase with the 3'-hydroxy group on ring A increases the selectivity of Compound A. C-C bond rotation around ring A also stabilizes and enhances the interaction of Compound A with butyrylcholinesterase. Furthermore, the classical network of hydrogen bonding interactions as formed by the catalytic triad of butyrylcholinesterase is disturbed by Compound A. This study may open a new avenue for structure-based drug design for Alzheimer's disease by considering the 3D-pharmacophoric features of the complex responsible for discriminating these two closely-related cholinesterases.</p

Learning, Memory, and the Role of Neural Network Architecture

The performance of information processing systems, from artificial neural networks to natural neuronal ensembles, depends heavily on the underlying system architecture. In this study, we compare the performance of parallel and layered network architectures during sequential tasks that require both acquisition and retention of information, thereby identifying tradeoffs between learning and memory processes. During the task of supervised, sequential function approximation, networks produce and adapt representations of external information. Performance is evaluated by statistically analyzing the error in these representations while varying the initial network state, the structure of the external information, and the time given to learn the information. We link performance to complexity in network architecture by characterizing local error landscape curvature. We find that variations in error landscape structure give rise to tradeoffs in performance; these include the ability of the network to maximize accuracy versus minimize inaccuracy and produce specific versus generalizable representations of information. Parallel networks generate smooth error landscapes with deep, narrow minima, enabling them to find highly specific representations given sufficient time. While accurate, however, these representations are difficult to generalize. In contrast, layered networks generate rough error landscapes with a variety of local minima, allowing them to quickly find coarse representations. Although less accurate, these representations are easily adaptable. The presence of measurable performance tradeoffs in both layered and parallel networks has implications for understanding the behavior of a wide variety of natural and artificial learning systems