A quasi-Riemannian approach to constrained optimization - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2016

A quasi-Riemannian approach to constrained optimization

Abstract

A quasi-Riemannian approach is developed for constrained optimization in which the retraction and transport operators are only approximate. If n is the dimension of the admissible domain, and p the number of scalar equality constraints, the iteration is expressed in terms of a vector of reduced dimension n − p lying in the subspace tangent to the constraint manifold as optimization variable, whereas the minimized function is evaluated at a point, after retraction, that is approximately on the constraint manifold. Precisely, if h is the norm of the tangent vector, the distance between the point of evaluation of the function to be minimized, after retraction, is in general O(h4), while it would only be O(h2) if retraction were not applied. The construction only requires evaluation procedures for constraint functions and their gradients to be provided, and eludes the necessity of curvature information.
Fichier principal
Vignette du fichier
RR-9007.pdf (844.36 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01417428 , version 1 (19-12-2016)

Identifiers

  • HAL Id : hal-01417428 , version 1

Cite

Jean-Antoine Désidéri. A quasi-Riemannian approach to constrained optimization. [Research Report] RR-9007, Inria Sophia Antipolis. 2016. ⟨hal-01417428⟩
192 View
65 Download

Share

Gmail Facebook Twitter LinkedIn More