Large-scale nonlinear programming algorithm using projection methods

Paweł Białoń

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2000)

  • Volume: 20, Issue: 2, page 171-194
  • ISSN: 1509-9407

Abstract

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A method for solving large convex optimization problems is presented. Such problems usually contain a big linear part and only a small or medium nonlinear part. The parts are tackled using two specialized (and thus efficient) external solvers: purely nonlinear and large-scale linear with a quadratic goal function. The decomposition uses an alteration of projection methods. The construction of the method is based on the zigzagging phenomenon and yields a non-asymptotic convergence, not dependent on a large dimension of the problem. The method preserves its convergence properties under limitations in complicating sets by geometric cuts. Various aspects and variants of the method are analyzed theoretically and experimentally.

How to cite

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Paweł Białoń. "Large-scale nonlinear programming algorithm using projection methods." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 20.2 (2000): 171-194. <http://eudml.org/doc/271430>.

@article{PawełBiałoń2000,
abstract = {A method for solving large convex optimization problems is presented. Such problems usually contain a big linear part and only a small or medium nonlinear part. The parts are tackled using two specialized (and thus efficient) external solvers: purely nonlinear and large-scale linear with a quadratic goal function. The decomposition uses an alteration of projection methods. The construction of the method is based on the zigzagging phenomenon and yields a non-asymptotic convergence, not dependent on a large dimension of the problem. The method preserves its convergence properties under limitations in complicating sets by geometric cuts. Various aspects and variants of the method are analyzed theoretically and experimentally.},
author = {Paweł Białoń},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {nonlinear optimization; large scale optimization; projection methods; zigzagging; numerical examples; large scale nonlinear optimization; feasibility problem; nonasymptotic convergence},
language = {eng},
number = {2},
pages = {171-194},
title = {Large-scale nonlinear programming algorithm using projection methods},
url = {http://eudml.org/doc/271430},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Paweł Białoń
TI - Large-scale nonlinear programming algorithm using projection methods
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2000
VL - 20
IS - 2
SP - 171
EP - 194
AB - A method for solving large convex optimization problems is presented. Such problems usually contain a big linear part and only a small or medium nonlinear part. The parts are tackled using two specialized (and thus efficient) external solvers: purely nonlinear and large-scale linear with a quadratic goal function. The decomposition uses an alteration of projection methods. The construction of the method is based on the zigzagging phenomenon and yields a non-asymptotic convergence, not dependent on a large dimension of the problem. The method preserves its convergence properties under limitations in complicating sets by geometric cuts. Various aspects and variants of the method are analyzed theoretically and experimentally.
LA - eng
KW - nonlinear optimization; large scale optimization; projection methods; zigzagging; numerical examples; large scale nonlinear optimization; feasibility problem; nonasymptotic convergence
UR - http://eudml.org/doc/271430
ER -

References

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