Invited Session Fri.1.H 0107

Friday, 10:30 - 12:00 h, Room: H 0107

Cluster 16: Nonlinear programming [...]

Optimality conditions and constraint qualifications

 

Chair: José Mario Martínez

 

 

Friday, 10:30 - 10:55 h, Room: H 0107, Talk 1

María Cristina Maciel
A trust region algorithm for the nonconvex unconstrained vector optimization problem

Coauthors: Gabriel A. Carrizo, Pablo A. Lotito

 

Abstract:
A trust-region-based algorithm for the non convex unconstrained vector optimization problem is
considered. It is a generalization of the algorithms proposed by Fliege, Graña Drumond and Svaiter
(2009) for the convex problem. Similarly to the scalar case, at each iteration, a trust region
subproblem is solved and the step is evaluated. The notions of decrease condition and of predicted
reduction are adapted to the vector case. A rule to update the trust region radius is introduced.
Under differentiability assumptions, the algorithm converges to a Pareto point satisfying a necessary condition and in the convex case to a Pareto point satisfying necessary and sufficient conditions like the procedure proposed by the cited authors.

 

 

Friday, 11:00 - 11:25 h, Room: H 0107, Talk 2

Paulo J. S. Silva
Constant positive generators: A new weak constraint qualification with algorithmic applications

Coauthors: Roberto Andreani, Gabriel Haeser, María L. Schuverdt

 

Abstract:
This talk introduces a generalization of the constant rank of the subspace component constraint qualification called the constant positive generator condition (CPG). This new constraint qualification is much weaker. For example, it can hold even in the absence of an error bound for the constraints and it can hold at a feasible point x while failing arbitrarily close to x.
In spite of its generality, it is possible to show that CPG is enough to ensure that almost-KKT points are actually KKT. Hence, this new condition can be used as a very mild assumption to assert the convergence of many algorithms to first order stationary points. As examples, we present extensions of convergence results for algorithms belonging to different classes of nonlinear optimization methods: augmented Lagrangians, inexact restoration, SQP, and interior point methods.

 

 

Friday, 11:30 - 11:55 h, Room: H 0107, Talk 3

Santosh Kumar Srivastav
Fritz John duality in the presence of equality and inequality constraints

 

Abstract:
A dual for a nonlinear programming problem in the presence of equality and inequality constraints is formulated which uses Fritz John optimality conditions instead of the Karush-Kuhn-Tucker optimality conditions and thus does not require a constraint qualifications. Various duality results, namely, weak, strong, strict converse and converse duality theorems are established under suitable generalized convexity assumptions.

 

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