# Large-scale nonlinear programming algorithm using projection methods

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

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

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topPaweł 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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