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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
A Predictor-Corrector Path-Following Algorithm for Dual-Degenerate Parametric Optimization Problems
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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