On the compatibility of classical multiplier estimates with variable reduction techniques when there are nonlinear inequality constraints.

Eugenio Mijangos Fernández; Narcís Nabona Francisco

Qüestiió (1999)

  • Volume: 23, Issue: 1, page 61-83
  • ISSN: 0210-8054

Abstract

top
The minimization of a nonlinear function subject to linear and nonlinear equality constraints and simple bounds can be performed through minimizing a partial augmented Lagrangian function subject only to linear constraints and simple bounds by variable reduction techniques. The first-order procedure for estimating the multiplier of the nonlinear equality constraints through the Kuhn-Tucker conditions is analyzed and compared to that of Hestenes-Powell. There is a method which identifies those major iterations where the procedure based on the Kuhn-Tucker conditions can be safely used and also computes these estimates. This work justifies the extension of the former results to the case of general inequality constraints. To this end two procedures that convert inequalities into equalities are considered.

How to cite

top

Mijangos Fernández, Eugenio, and Nabona Francisco, Narcís. "On the compatibility of classical multiplier estimates with variable reduction techniques when there are nonlinear inequality constraints.." Qüestiió 23.1 (1999): 61-83. <http://eudml.org/doc/40272>.

@article{MijangosFernández1999,
abstract = {The minimization of a nonlinear function subject to linear and nonlinear equality constraints and simple bounds can be performed through minimizing a partial augmented Lagrangian function subject only to linear constraints and simple bounds by variable reduction techniques. The first-order procedure for estimating the multiplier of the nonlinear equality constraints through the Kuhn-Tucker conditions is analyzed and compared to that of Hestenes-Powell. There is a method which identifies those major iterations where the procedure based on the Kuhn-Tucker conditions can be safely used and also computes these estimates. This work justifies the extension of the former results to the case of general inequality constraints. To this end two procedures that convert inequalities into equalities are considered.},
author = {Mijangos Fernández, Eugenio, Nabona Francisco, Narcís},
journal = {Qüestiió},
keywords = {Programación no lineal; Multiplicadores de Lagrange; nonlinear programming; general inequality constraints; augmented Lagrangian; variable reduction; Lagrange multiplier estimates},
language = {eng},
number = {1},
pages = {61-83},
title = {On the compatibility of classical multiplier estimates with variable reduction techniques when there are nonlinear inequality constraints.},
url = {http://eudml.org/doc/40272},
volume = {23},
year = {1999},
}

TY - JOUR
AU - Mijangos Fernández, Eugenio
AU - Nabona Francisco, Narcís
TI - On the compatibility of classical multiplier estimates with variable reduction techniques when there are nonlinear inequality constraints.
JO - Qüestiió
PY - 1999
VL - 23
IS - 1
SP - 61
EP - 83
AB - The minimization of a nonlinear function subject to linear and nonlinear equality constraints and simple bounds can be performed through minimizing a partial augmented Lagrangian function subject only to linear constraints and simple bounds by variable reduction techniques. The first-order procedure for estimating the multiplier of the nonlinear equality constraints through the Kuhn-Tucker conditions is analyzed and compared to that of Hestenes-Powell. There is a method which identifies those major iterations where the procedure based on the Kuhn-Tucker conditions can be safely used and also computes these estimates. This work justifies the extension of the former results to the case of general inequality constraints. To this end two procedures that convert inequalities into equalities are considered.
LA - eng
KW - Programación no lineal; Multiplicadores de Lagrange; nonlinear programming; general inequality constraints; augmented Lagrangian; variable reduction; Lagrange multiplier estimates
UR - http://eudml.org/doc/40272
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.