Quasidifferentiability of real-valued functions and local extremum conditions

1985 ◽  
Vol 25 (3) ◽  
pp. 388-395
Author(s):  
V. V. Gorokhovik
Keyword(s):  
Local Extremum ◽  
Extremum Conditions

scholarly journals A bat optimization algorithm with moderate orientation and perturbation of trend

2021 ◽  
Vol 15 ◽  
pp. 174830262110084
Author(s):  
Jingsen Liu ◽  
Hongyuan Ji ◽  
Qingqing Liu ◽  
Yu Li
Keyword(s):  
Local Search ◽  
Optimization Algorithm ◽  
Random Perturbation ◽  
Bat Algorithm ◽  
Local Extremum ◽  
Global Search ◽  
Deep Mining ◽  
Nonlinear Variation ◽  
Optimal Value ◽  
Search Stage

In order to improve the convergence speed and optimization accuracy of the bat algorithm, a bat optimization algorithm with moderate optimal orientation and random perturbation of trend is proposed. The algorithm introduces the nonlinear variation factor into the velocity update formula of the global search stage to maintain a high diversity of bat populations, thereby enhanced the global exploration ability of the algorithm. At the same time, in the local search stage, the position update equation is changed, and a strategy that towards optimal value modestly is used to improve the ability of the algorithm to local search for deep mining. Finally, the adaptive decreasing random perturbation is performed on each bat individual that have been updated in position at each generation, which can improve the ability of the algorithm to jump out of the local extremum, and to balance the early global search extensiveness and the later local search accuracy. The simulating results show that the improved algorithm has a faster optimization speed and higher optimization accuracy.

An Adaptive Invasive Weed Optimization Algorithm

2015 ◽  
Vol 29 (02) ◽  
pp. 1559004 ◽  
Author(s):  
Shuo Peng ◽  
A.-J. Ouyang ◽  
Jeff Jun Zhang
Keyword(s):  
Optimization Algorithm ◽  
Initial Step ◽  
Local Extremum ◽  
Invasive Weed Optimization ◽  
Step Size ◽  
Invasive Weed ◽  
Adaptive Step Size ◽  
Initial Step Size ◽  
Adaptive Step ◽  
Optimization Search

With regards to the low search accuracy of the basic invasive weed optimization algorithm which is easy to get into local extremum, this paper proposes an adaptive invasive weed optimization (AIWO) algorithm. The algorithm sets the initial step size and the final step size as the adaptive step size to guide the global search of the algorithm, and it is applied to 20 famous benchmark functions for a test, the results of which show that the AIWO algorithm owns better global optimization search capacity, faster convergence speed and higher computation accuracy compared with other advanced algorithms.

scholarly journals A New Fruit Fly Optimization Algorithm Based on Differential Evolution

2015 ◽  
Vol 3 (4) ◽  
pp. 365-373 ◽  
Author(s):  
Dabin Zhang ◽  
Jia Ye ◽  
Zhigang Zhou ◽  
Yuqi Luan
Keyword(s):  
Differential Evolution ◽  
Optimization Algorithm ◽  
Fruit Fly ◽  
Local Extremum ◽  
Experimental Results ◽  
Fruit Fly Optimization Algorithm ◽  
A Algorithm ◽  
Fruit Fly Optimization ◽  
Searching Ability ◽  
Selection Of

Abstract In order to overcome the problem of low convergence precision and easily relapsing into local extremum in fruit fly optimization algorithm (FOA), this paper adds the idea of differential evolution to fruit fly optimization algorithm so as to optimizing and a algorithm of fruit fly optimization based on differential evolution is proposed (FOADE). Adding the operating of mutation, crossover and selection of differential evolution to FOA after each iteration, which can jump out local extremum and continue to optimize. Compared to FOA, the experimental results show that FOADE has the advantages of better global searching ability, faster convergence and more precise convergence.

scholarly journals Nondestructive Identification of Salmon Adulteration with Water Based on Hyperspectral Data

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Tao Zhang ◽  
Biyao Wang ◽  
Pengtao Yan ◽  
Kunlun Wang ◽  
Xu Zhang ◽  
...  
Keyword(s):  
Near Infrared ◽  
Water Injection ◽  
Principal Component ◽  
Local Extremum ◽  
Hyperspectral Data ◽  
Identification Accuracy ◽  
Hyperspectral Images ◽  
Nondestructive Identification ◽  
Som Network ◽  
Weighting Coefficients

For the identification of salmon adulteration with water injection, a nondestructive identification method based on hyperspectral images was proposed. The hyperspectral images of salmon fillets in visible and near-infrared ranges (390–1050 nm) were obtained with a system. The original hyperspectral data were processed through the principal-component analysis (PCA). According to the image quality and PCA parameters, a second principal-component (PC2) image was selected as the feature image, and the wavelengths corresponding to the local extremum values of feature image weighting coefficients were extracted as feature wavelengths, which were 454.9, 512.3, and 569.1 nm. On this basis, the color combined with spectra at feature wavelengths, texture combined with spectra at feature wavelengths, and color-texture combined with spectra at feature wavelengths were independently set as the input, for the modeling of salmon adulteration identification based on the self-organizing feature map (SOM) network. The distances between neighboring neurons and feature weights of the models were analyzed to realize the visualization of identification results. The results showed that the SOM-based model, with texture-color combined with fusion features of spectra at feature wavelengths as the input, was evaluated to possess the best performance and identification accuracy is as high as 96.7%.

scholarly journals Optimized random-phase approximations for arbitrary reference systems: Extremum conditions and thermodynamic consistence

1998 ◽  
Vol 57 (1) ◽  
pp. 460-464 ◽  
Author(s):  
G. Pastore ◽  
O. Akinlade ◽  
F. Matthews ◽  
Z. Badirkhan
Keyword(s):  
Random Phase ◽  
Reference Systems ◽  
Arbitrary Reference ◽  
Extremum Conditions

An Experimental Study of Plane Plumes in Cold Water

1983 ◽  
Vol 105 (2) ◽  
pp. 248-254 ◽  
Author(s):  
Y. Joshi ◽  
B. Gebhart
Keyword(s):  
Buoyancy Force ◽  
Cold Water ◽  
Pure Water ◽  
Density Variation ◽  
Complex Flow ◽  
Flow Temperature ◽  
Ambient Temperatures ◽  
Density Relation ◽  
Convective Motions ◽  
Extremum Conditions

The peculiar density variation of water with temperature makes the Boussinesq approximations invalid in the vicinity of density extremum conditions. The buoyancy force reversals which often arise from the density extremum have been studied in many recent investigations. The formulation of an accurate density relation has resulted in a simplified analysis for many convective motions. Two such analyses have dealt with the flow generated above a heated line source in cold water, around the extremum point. We present an experimental investigation of such flow. Temperature measurements have been carried out for ambient temperatures, t∞ ≥ tm, the temperature of density extremum, for pure water at atmospheric pressure. These measurements are in satisfactory agreement with the analyses. As the ambient temperature is successively increased above the density extremum temperature, the transformation of the flow behaviour from non-Boussinesq to Boussinesq is very clearly observed. Velocity measurements have been made at t∞=4°C, the extremum temperature. For t∞<tm, very complex flow patterns exist, due to the bidirectional buoyancy force. These patterns have been visualized. The influence of a bounding impermeable surface below the plume source has also been examined.

A comprehensive approach for optimal design of magnetorheological dampers

2018 ◽  
Vol 29 (18) ◽  
pp. 3648-3655 ◽  
Author(s):  
Mohammad Mehdi Naserimojarad ◽  
Mehrdad Moallem ◽  
Siamak Arzanpour
Keyword(s):  
Optimal Design ◽  
Vibration Suppression ◽  
Mathematical Optimization ◽  
Optimization Method ◽  
Global Optimum ◽  
Local Extremum ◽  
Magnetorheological Damper ◽  
Magnetorheological Dampers ◽  
Global Extremum ◽  
Element Analysis

Magnetorheological dampers have been used in automotive industry and civil engineering applications for shock and vibration control for some time. While such devices are known to provide reliable shock and vibration suppression, there exist emerging applications in which the magnetorheological dampers have to be optimized in terms of power consumption and overall weight (e.g. energy-efficient electric vehicles). Utilizing traditional optimal design approaches to tackle those issues can sometimes lead to convergence problems such as getting trapped in a local extremum and failing to converge to the global optimum. Furthermore, manufacturing limitations are usually not taken into account in the optimization process which may hamper achieving an optimal design. In this article, we present a method for optimal design of magnetorheological dampers by utilizing mathematical optimization and finite element analysis. The proposed method avoids infeasible solutions by considering physical constraints such as fabrication limitations and tolerances. This approach takes every single feasible solution into account so that the final solution would be the global extremum of the optimization cost function. The proposed approach is applied to optimize a complex magnetorheological damper structure with different types of materials such as steel and AlNiCo. In particular, we present the design of a valve-mode magnetorheological damper with AlNiCo integrated as its core. A magnetorheological damper prototype is manufactured based on the proposed optimization method and tested experimentally.

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