Variational perturbations of the minimum effort problem

1980 ◽  
Vol 30 (3) ◽  
pp. 485-499 ◽  
Author(s):  
R. Lucchetti ◽  
F. Mignanego
Keyword(s):  
Variational Perturbations

A concept of inner prederivative for set-valued mappings and its applications

2018 ◽  
Vol 24 (3) ◽  
pp. 1059-1074
Author(s):  
Michel H. Geoffroy ◽  
Yvesner Marcelin
Keyword(s):  
Optimality Conditions ◽  
Necessary Optimality Conditions ◽  
Welfare Economics ◽  
Inverse Mapping ◽  
First Order ◽  
Inverse Mapping Theorem ◽  
Homogeneous Set ◽  
Optimal Allocations ◽  
Variational Perturbations ◽  
Set Valued Mappings

We introduce a class of positively homogeneous set-valued mappings, called inner prederivatives, serving as first order approximants to set-valued mappings. We prove an inverse mapping theorem involving such prederivatives and study their stability with respect to variational perturbations. Then, taking advantage of their properties we establish necessary optimality conditions for the existence of several kind of minimizers in set-valued optimization. As an application of these last results, we consider the problem of finding optimal allocations in welfare economics. Finally, to emphasize the interest of our approach, we compare the notion of inner prederivative to the related concepts of set-valued differentiation commonly used in the literature.

Sign in / Sign up

Export Citation Format

Share Document