Second-order characterization of convex functions and its applications

2019 ◽  
Vol 25 (1) ◽  
pp. 49-58
Author(s):  
Mohammad Taghi Nadi ◽  
Jen Chih Yao ◽  
Jafar Zafarani
Keyword(s):  
Convex Functions ◽  
Optimization Problems ◽  
Second Order ◽  
Subdifferential Mapping

Abstract Some developments of the second-order characterizations of convex functions are investigated by using the coderivative of the subdifferential mapping. Furthermore, some applications of the second-order subdifferentials in optimization problems are studied.

scholarly journals Search Patterns Based on Trajectories Extracted from the Response of Second-Order Systems

2021 ◽  
Vol 11 (8) ◽  
pp. 3430
Author(s):  
Erik Cuevas ◽  
Héctor Becerra ◽  
Héctor Escobar ◽  
Alberto Luque-Chang ◽  
Marco Pérez ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Second Order ◽  
Order System ◽  
Search Patterns ◽  
Multiple Behaviors ◽  
Complex Optimization ◽  
Second Order Systems ◽  
Order Algorithm

Recently, several new metaheuristic schemes have been introduced in the literature. Although all these approaches consider very different phenomena as metaphors, the search patterns used to explore the search space are very similar. On the other hand, second-order systems are models that present different temporal behaviors depending on the value of their parameters. Such temporal behaviors can be conceived as search patterns with multiple behaviors and simple configurations. In this paper, a set of new search patterns are introduced to explore the search space efficiently. They emulate the response of a second-order system. The proposed set of search patterns have been integrated as a complete search strategy, called Second-Order Algorithm (SOA), to obtain the global solution of complex optimization problems. To analyze the performance of the proposed scheme, it has been compared in a set of representative optimization problems, including multimodal, unimodal, and hybrid benchmark formulations. Numerical results demonstrate that the proposed SOA method exhibits remarkable performance in terms of accuracy and high convergence rates.

scholarly journals Pointwise estimates for higher order convexity preserving polynomial approximation

1994 ◽  
Vol 36 (2) ◽  
pp. 213-233 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska
Keyword(s):  
Polynomial Approximation ◽  
Convex Functions ◽  
Higher Order ◽  
Second Order ◽  
Convolution Type ◽  
Shape Preservation ◽  
Moduli Of Continuity ◽  
Pointwise Estimates ◽  
Higher Order Convexity ◽  
Boolean Sum

AbstractDeVore-Gopengauz-type operators have attracted some interest over the recent years. Here we investigate their relationship to shape preservation. We construct certain positive convolution-type operators Hn, s, j which leave the cones of j-convex functions invariant and give Timan-type inequalities for these. We also consider Boolean sum modifications of the operators Hn, s, j show that they basically have the same shape preservation behavior while interpolating at the endpoints of [−1, 1], and also satisfy Telyakovskiῐ- and DeVore-Gopengauz-type inequalities involving the first and second order moduli of continuity, respectively. Our results thus generalize related results by Lorentz and Zeller, Shvedov, Beatson, DeVore, Yu and Leviatan.

PMD Characterization of a Dispersion Managed Link up to the Second-order with High Accuracy

2006 ◽  
Vol 38 (7) ◽  
pp. 575-582
Author(s):  
O. M. Diaz ◽  
J. Prat ◽  
I. Tafur Monroy ◽  
H. de Waardt
Keyword(s):  
High Accuracy ◽  
Second Order

scholarly journals Fabrication and characterization of periodically patterned silica fiber structures for enhanced second-order nonlinearity: publisher’s note

2017 ◽  
Vol 25 (9) ◽  
pp. 10473
Author(s):  
Chalongrat Daengngam ◽  
Ishac Kandas ◽  
Islam Ashry ◽  
Jeong-Ah Lee ◽  
Anbo Wang ◽  
...  
Keyword(s):  
Second Order ◽  
Silica Fiber ◽  
Fabrication And Characterization ◽  
Second Order Nonlinearity

scholarly journals Synthesis and characterization of novel second-order NLO-chromophores bearing pyrrole as an electron donor group

Tetrahedron ◽  
2012 ◽  
Vol 68 (39) ◽  
pp. 8147-8155 ◽  
Author(s):  
M. Cidália R. Castro ◽  
M. Belsley ◽  
A. Maurício C. Fonseca ◽  
M. Manuela M. Raposo
Keyword(s):  
Electron Donor ◽  
Second Order ◽  
Synthesis And Characterization ◽  
Donor Group ◽  
Nlo Chromophores
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