Optimization in the Heisenberg group

In this article, the local unconstrained and the constrained optimization problems in the Heisenberg group are investigated. The framework on which we work is given by the class of weakly H-convex functions recently introduced in the literature. This geometric notion of convexity, that is strictly r...

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Bibliographic Details
Published in:Optimization Vol. 55; no. 4; pp. 387 - 403
Main Authors: Calogero, A., Carcano, G., Pini, R.
Format: Journal Article
Language:English
Published: Taylor & Francis Group 01.08.2006
Subjects:
Convexity
Horizontal gradient
Horizontal Hessian
Mathematics
Mathematics Subject Classifications 2000: 90C26
Non-linear
Optimality conditions
OR/MS Subject Classifications: Primary: Programming
Theory
Twisted convex combination
Weak H-convexity
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:In this article, the local unconstrained and the constrained optimization problems in the Heisenberg group are investigated. The framework on which we work is given by the class of weakly H-convex functions recently introduced in the literature. This geometric notion of convexity, that is strictly related to the stratified structure of the group and has not an analogous in a Euclidean setting, requires a condition of convexity to be satisfied at the points of the horizontal planes. We find second-order sufficient conditions for a local extremum in both the unconstrained and the constrained optimization problems exploiting the weak H-convexity and the geometric behaviour of the horizontal planes in .
ISSN:0233-1934
1029-4945
DOI:10.1080/02331930600662880