Contributed Session Fri.1.H 2035

Friday, 10:30 - 12:00 h, Room: H 2035

Cluster 24: Variational analysis [...]

Variational-analytic foundations of sensitivity analysis

 

Chair: Dmitriy Drusvyatskiy

 

 

Friday, 10:30 - 10:55 h, Room: H 2035, Talk 1

Shanshan Zhang
Partial smoothness, tilt stability, and generalized Hessians

Coauthor: Adrian S. Lewis

 

Abstract:
We compare two recent variational-analytic approaches to second-order conditions and sensitivity analysis for nonsmooth optimization. We describe a broad setting where computing the generalized Hessian of Mordukhovich is easy. In this setting, the idea of tilt stability introduced by Poliquin and Rockafellar is equivalent to a classical smooth second-order condition.

 

 

Friday, 11:00 - 11:25 h, Room: H 2035, Talk 2

Iqbal Husain
On second-order Fritz John type duality for variational problems

Coauthor: Santosh Kumar Srivastav

 

Abstract:
A second-order dual to a variational problem is formulated. This dual uses the Fritz John type necessary optimality conditions instead of the Karush-Kuhn-Tucker type necessary optimality conditions and thus, does not require a constraint qualification. Weak, strong, Mangasarian type strict-converse, and Huard type converse duality theorems between primal and dual problems are established. A pair of second-order dual variational problems with natural boundary conditions is constructed, and it is briefly indicated that the duality results for this pair can be validated analogously to those for the earlier models dealt with in this research. Finally, it is pointed out that our results can be viewed as the dynamic generalizations of those for nonlinear programming problems, already treated in the literature.

 

 

Friday, 11:30 - 11:55 h, Room: H 2035, Talk 3

Dmitriy Drusvyatskiy
Identifiability and the foundations of sensitivity analysis

Coauthor: Adrian S. Lewis

 

Abstract:
Given a solution to some optimization problem, an identifiable subset of the feasible region is one that captures all of the problem's behavior under small perturbations. Seeking only the most essential ingredients of sensitivity analysis leads to identifiable sets that are in a sense minimal. In particular, critical cones - objects of classical importance - have an intuitive interpretation as tangential approximations to such sets. I will discuss how this new notion leads to a broad (and intuitive) variational-analytic foundation underlying active sets and their role in sensitivity analysis.

 

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