The lagrange multiplier set and the generalized gradient set of the marginal function of a differentiable program in a Banach space

1982 ◽  
Vol 38 (3) ◽  
pp. 307-317 ◽  
Author(s):  
J. C. Pomerol
Keyword(s):  
Banach Space ◽  
Lagrange Multiplier ◽  
Marginal Function ◽  
Generalized Gradient

scholarly journals Quasi-regularity in Optimization

1986 ◽  
Vol 41 (2) ◽  
pp. 188-192 ◽  
Author(s):  
Kung-Fu Ng ◽  
David Yost
Keyword(s):  
Banach Space ◽  
Lagrange Multiplier ◽  
Optimization Problems ◽  
General Situation ◽  
Lagrange Multiplier Rule ◽  
Infinite Dimensional ◽  
Space Setting ◽  
Multiplier Rule ◽  
Dimensional Version ◽  
Definition Of

AbstractThe notion of quasi-regularity, defined for optimization problems in Rn, is extended to the Banach space setting. Examples are given to show that our definition of quasi-regularity is more natural than several other possibilities in the general situation. An infinite dimensional version of the Lagrange multiplier rule is established.

The Proximal Subgradient Formula in Banach Space

1988 ◽  
Vol 31 (3) ◽  
pp. 353-361 ◽  
Author(s):  
Philip D. Loewen
Keyword(s):  
Banach Space ◽  
Lower Semicontinuous ◽  
Lower Semicontinuous Function ◽  
Semicontinuous Function ◽  
Generalized Gradient ◽  
Infinite Dimensional ◽  
Fréchet Differentiable ◽  
The One ◽  
The Given ◽  
Normal Formula

AbstractThe proximal subgradient formula is a refinement due to Rockafellar of Clarke's fundamental proximal normal formula. It expresses Clarke's generalized gradient of a lower semicontinuous function in terms of analytically simpler proximal subgradients. We use the infinite-dimensional proximal normal formula recently given by Borwein and Strojwas to derive a new version of the proximal subgradient formula in a reflexive Banach space X with Frechet differentiable and locally uniformly convex norm. Our result improves on the one given by Borwein and Strojwas by referring only to the given norm on X.

Interstitial vs. Substitutional Metal Insertion in V2O5 as Post-Lithium Ion Battery Cathode: A Comparative GGA/GGA+U Study with Localized Bases

2020 ◽  
Author(s):  
Daniel Koch ◽  
Sergei Manzhos
Keyword(s):  
Electronic Structure ◽  
Plane Wave ◽  
Transition Metal Oxides ◽  
Reasonable Agreement ◽  
Correction Term ◽  
Lithium Ion ◽  
Generalized Gradient ◽  
Main Group Metals ◽  
Generalized Gradient Approximation ◽  
Metal Insertion

<p></p><p>The generalized gradient approximation (GGA) often fails to correctly describe the electronic structure and thermochemistry of transition metal oxides and is commonly improved using an inexpensive correction term with a scaling parameter <i>U</i>. We tune <i>U</i> to reproduce experimental vanadium oxide redox energetics with a localized basis and a GGA functional. We find the value for <i>U</i> to be significantly lower than what is generally reported with plane-wave bases, with the uncorrected GGA results being in reasonable agreement with experiments. We use this computational setup to calculate interstitial and substitutional <a>insertion energies of main group metals in vanadium pentoxide</a> and find <a>interstitial doping to be thermodynamically favored</a>.</p><p></p>

Ab initio calculation on the Optical Properties of AA- Stacked two dimensional Graphene, Silicene, Germanene, and Stanene

2018 ◽  
Vol 1 (1) ◽  
pp. 46-50
Author(s):  
Rita John ◽  
Benita Merlin
Keyword(s):  
Optical Properties ◽  
Band Structure ◽  
Density Functional ◽  
Electronic Band Structure ◽  
Complex Refractive Index ◽  
Single Layer ◽  
Generalized Gradient ◽  
Electronic Band ◽  
Wide Range ◽  
Optical Region

In this study, we have analyzed the electronic band structure and optical properties of AA-stacked bilayer graphene and its 2D analogues and compared the results with single layers. The calculations have been done using Density Functional Theory with Generalized Gradient Approximation as exchange correlation potential as in CASTEP. The study on electronic band structure shows the splitting of valence and conduction bands. A band gap of 0.342eV in graphene and an infinitesimally small gap in other 2D materials are generated. Similar to a single layer, AA-stacked bilayer materials also exhibit excellent optical properties throughout the optical region from infrared to ultraviolet. Optical properties are studied along both parallel (||) and perpendicular ( ) polarization directions. The complex dielectric function (ε) and the complex refractive index (N) are calculated. The calculated values of ε and N enable us to analyze optical absorption, reflectivity, conductivity, and the electron loss function. Inferences from the study of optical properties are presented. In general the optical properties are found to be enhanced compared to its corresponding single layer. The further study brings out greater inferences towards their direct application in the optical industry through a wide range of the optical spectrum.

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