-

 

 

 




Optimization Online





 

A Special Complementarity Function Revisited

Roger Behling (roger.behling***at***ufsc.br)
Andreas Fischer (Andreas.Fischer***at***tu-dresden.de)
Klaus Schönefeld (Klaus.Schoenefeld***at***tu-dresden.de)
Nico Strasdat (Nico.Strasdat***at***tu-dresden.de)

Abstract: Recently, a local framework of Newton-type methods for constrained systems of equations has been developed which, applied to the solution of Karush-KuhnTucker (KKT) systems, enables local quadratic convergence under conditions that allow nonisolated and degenerate KKT points. This result is based on a reformulation of the KKT conditions as a constrained piecewise smooth system of equations. It is an open question whether a comparable result can be achieved for other (not piecewise smooth) reformulations. It will be shown that this is possible if the KKT system is reformulated by means of the Fischer-Burmeister complementarity function under conditions that allow degenerate KKT points and nonisolated Lagrange multipliers. To obtain this result, novel constrained Levenberg-Marquardt subproblems are introduced which allow significantly longer steps for updating the multipliers. Based on this, a convergence rate of at least 1.5 is shown.

Keywords: Karush-Kuhn-Tucker system, nonunique multipliers, degenerate solution, constrained Levenberg-Marquardt method

Category 1: Complementarity and Variational Inequalities

Category 2: Nonlinear Optimization

Citation: Optimzation, https://doi.org/10.1080/02331934.2018.1470177, Technical Report: MATH-NM-06-2017, Institute of Numerical Mathematics, Faculty of Mathematics, TU Dresden, Germany, December 2017

Download: [PDF]

Entry Submitted: 04/27/2018
Entry Accepted: 05/01/2018
Entry Last Modified: 06/08/2018

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