scholarly journals Qualification Conditions in Semialgebraic Programming

2018 ◽  
Vol 28 (2) ◽  
pp. 1867-1891 ◽  
Author(s):  
Jérôme Bolte ◽  
Antoine Hochart ◽  
Edouard Pauwels
Keyword(s):  
Qualification Conditions

On Second-Order Composed Proto-Differentiability of Proper Perturbation Maps in Parametric Vector Optimization Problems

2020 ◽  
pp. 2050040
Author(s):  
Le Thanh Tung
Keyword(s):  
Vector Optimization ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Second Order ◽  
Vector Optimization Problems ◽  
Solution Maps ◽  
Qualification Conditions ◽  
Parametric Vector Optimization ◽  
Perturbation Maps ◽  
Proper Efficient Solution

The main aim of this paper is to study second-order sensitivity analysis in parametric vector optimization problems. We prove that the proper perturbation maps and the proper efficient solution maps of parametric vector optimization problems are second-order composed proto-differentiable under some appropriate qualification conditions. Some examples are provided to illustrate our results.

On M-stationarity conditions in MPECs and the associated qualification conditions

2017 ◽  
Vol 168 (1-2) ◽  
pp. 229-259 ◽  
Author(s):  
Lukáš Adam ◽  
René Henrion ◽  
Jiří Outrata
Keyword(s):  
Qualification Conditions ◽  
Stationarity Conditions

A Vectorized Regularization Method for Multivalued Parameters Identification

2019 ◽  
Vol 16 (07) ◽  
pp. 1850110 ◽  
Author(s):  
Abdellatif Ellabib ◽  
Youssef Ouakrim
Keyword(s):  
Minimization Problem ◽  
Regularization Method ◽  
Dual Problem ◽  
Conjugate Functions ◽  
Primal Problem ◽  
Dispersion Tensor ◽  
Qualification Conditions ◽  
Primal Dual ◽  
Constraint Minimization ◽  
Stability Of The Solution

The identification of multivalued parameters is formulated as a constraint minimization problem called primal problem. We embed it in a family of perturbed problems and we associate a dual problem with it using the conjugate functions. Basing on the primal-dual relationship, under some qualification conditions on the parameters to be identified we elaborate the well posedeness, convergence and stability of the solution assuming. Numerical simulations are described in the end for the identification of discontinuous dispersion tensor in transport equations.

scholarly journals A comparison of constraint qualifications in infinite-dimensional convex programming revisited

1999 ◽  
Vol 40 (3) ◽  
pp. 353-378 ◽  
Author(s):  
C. Zặlinescu
Keyword(s):  
Convex Programming ◽  
Constraint Qualification ◽  
Constraint Qualifications ◽  
Strong Duality ◽  
Sufficient Condition ◽  
Subdifferential Calculus ◽  
Infinite Dimensional ◽  
Qualification Conditions ◽  
The One

In 1990 Gowda and Teboulle published the paper [16], making a comparison of several conditions ensuring the Fenchel-Rockafellar duality formulainf{f(x) + g(Ax) | x ∈ X} = max{−f*(A*y*) − g*(− y*) | y* ∈ Y*}.Probably the first comparison of different constraint qualification conditions was made by Hiriart-Urruty [17] in connection with ε-subdifferential calculus. Among them appears, as the basic sufficient condition, the formula for the conjugate of the corresponding function; such functions are: f1 + f2, g o A, max{fl,…, fn}, etc. In fact strong duality formulae (like the one above) and good formulae for conjugates are equivalent and they can be used to obtain formulae for ε-subdifferentials, using a technique developed in [17] and extensively used in [46].

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