A Predictor-Corrector Path-Following Algorithm for Dual-Degenerate Parametric Optimization Problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F17%3A00316680" target="_blank" >RIV/68407700:21230/17:00316680 - isvavai.cz</a>

Výsledek na webu

<a href="http://epubs.siam.org/doi/pdf/10.1137/16M1068736" target="_blank" >http://epubs.siam.org/doi/pdf/10.1137/16M1068736</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/16M1068736" target="_blank" >10.1137/16M1068736</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Predictor-Corrector Path-Following Algorithm for Dual-Degenerate Parametric Optimization Problems

Popis výsledku v původním jazyce

Most path-following algorithms for tracing a solution path of a parametric nonlinear optimization problem are only certifiably convergent under strong regularity assumptions about the problem functions. In particular, linear independence of the constraint gradients at the solutions is typically assumed, which implies unique multipliers. In this paper we propose a procedure designed to solve problems satisfying a weaker set of conditions, allowing for nonunique (but bounded) multipliers. Each iteration along the path consists of three parts: (1) a Newton corrector step for the primal and dual variables, which is obtained by solving a linear system of equations, (2) a predictor step for the primal and dual variables, which is found as the solution of a quadratic programming problem, and (3) a jump step for the dual variables, which is found as the solution of a linear programming problem. We present a convergence proof and demonstrate the successful solution tracking of the algorithm numerically on a couple of illustrative examples.

Název v anglickém jazyce

A Predictor-Corrector Path-Following Algorithm for Dual-Degenerate Parametric Optimization Problems

Popis výsledku anglicky

Most path-following algorithms for tracing a solution path of a parametric nonlinear optimization problem are only certifiably convergent under strong regularity assumptions about the problem functions. In particular, linear independence of the constraint gradients at the solutions is typically assumed, which implies unique multipliers. In this paper we propose a procedure designed to solve problems satisfying a weaker set of conditions, allowing for nonunique (but bounded) multipliers. Each iteration along the path consists of three parts: (1) a Newton corrector step for the primal and dual variables, which is obtained by solving a linear system of equations, (2) a predictor step for the primal and dual variables, which is found as the solution of a quadratic programming problem, and (3) a jump step for the dual variables, which is found as the solution of a linear programming problem. We present a convergence proof and demonstrate the successful solution tracking of the algorithm numerically on a couple of illustrative examples.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM JOURNAL ON OPTIMIZATION

ISSN

1052-6234

e-ISSN

1095-7189

Svazek periodika

27

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

538-564

Kód UT WoS článku

000404178500023

EID výsledku v databázi Scopus

2-s2.0-85021144866