-

 

 

 




Optimization Online





 

Primal-dual relationship between Levenberg-Marquardt and central trajectories for linearly constrained convex optimization

Roger Behling (rogerbehling***at***gmail.com)
Clovis Gonzaga (clovis***at***mtm.ufsc.br)
Gabriel Haeser (gabriel.haeser***at***unifesp.br)

Abstract: We consider the minimization of a convex function on a compact polyhedron defined by linear equality constraints and nonnegative variables. We define the Levenberg-Marquardt (L-M) and central trajectories starting at the analytic center and using the same parameter, and show that they satisfy a primal-dual relationship, being close to each other for large values of the parameter. Based on this we develop an algorithm that starts computing primal-dual feasible points on the L-M trajectory and eventually moves to the central path. Our main theorem is particularly relevant in quadratic programming, where points on the primal-dual L-M trajectory can be calculated by means of a system of linear equations. We present some computational tests related to box constrained trust region subproblems.

Keywords: central path, Levenberg-Marquardt, primal-dual, interior points, convex quadratic programming, trust region, initial point

Category 1: Nonlinear Optimization (Quadratic Programming )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation:

Download: [PDF]

Entry Submitted: 09/05/2012
Entry Accepted: 09/05/2012
Entry Last Modified: 03/21/2013

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society