scholarly journals Bilevel Optimization and Variational Analysis

2020 ◽  
pp. 197-226
Author(s):  
Boris S. Mordukhovich
Keyword(s):  
Variational Analysis ◽  
Bilevel Optimization

scholarly journals R-Regularity of Set-Valued Mappings Under the Relaxed Constant Positive Linear Dependence Constraint Qualification with Applications to Parametric and Bilevel Optimization

2021 ◽  
Author(s):  
Patrick Mehlitz ◽  
Leonid I. Minchenko
Keyword(s):  
Linear Dependence ◽  
Constraint Qualification ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Bilevel Optimization ◽  
Regularity Property ◽  
Constant Rank Constraint Qualification ◽  
Existence Criterion ◽  
Set Valued Mappings

AbstractThe presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of, e.g., stability analysis or bilevel optimization. An example of such a Lipschitzian property for set-valued mappings, whose graph is the solution set of a system of nonlinear inequalities and equations, is R-regularity. Based on the so-called relaxed constant positive linear dependence constraint qualification, we provide a criterion ensuring the presence of the R-regularity property. In this regard, our analysis generalizes earlier results of that type which exploited the stronger Mangasarian–Fromovitz or constant rank constraint qualification. Afterwards, we apply our findings in order to derive new sufficient conditions which guarantee the presence of R-regularity for solution mappings in parametric optimization. Finally, our results are used to derive an existence criterion for solutions in pessimistic bilevel optimization and a sufficient condition for the presence of the so-called partial calmness property in optimistic bilevel optimization.

scholarly journals Recent development in nonlinear and variational analysis and optimization

Optimization ◽  
2021 ◽  
Vol 70 (4) ◽  
pp. 689-692
Author(s):  
Elisabeth Köbis ◽  
Jinlu Li ◽  
Adrian Petruşel ◽  
Jen-Chih Yao
Keyword(s):  
Variational Analysis ◽  
Variational Analysis And Optimization

Prediction of a Billet Shape for Axisymmetric Warm Forming Using Variational Analysis

2004 ◽  
Vol 274-276 ◽  
pp. 733-738 ◽  
Author(s):  
Ting Fai Kong ◽  
Luen Chow Chan ◽  
Tai Chiu Lee
Keyword(s):  
Variational Analysis ◽  
Warm Forming ◽  
Billet Shape

scholarly journals Variational analysis of HF dimer tunneling rotational spectra using an ab initio potential energy surface

2021 ◽  
pp. 111481
Author(s):  
Oleg L. Polyansky ◽  
Roman I. Ovsyannikov ◽  
Jonathan Tennyson ◽  
Sergei P. Belov ◽  
Mikhail Yu. Tretyakov ◽  
...  
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Variational Analysis ◽  
Energy Surface ◽  
Rotational Spectra
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