A modified search direction method with weakly imposed Karush-Kuhn-Tucker conditions for gradient based constraint optimization for very large problems

Long Chen, Armin Geiser, Roland Wüchner, Kai Uwe Bletzinger

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Motivated by the applications of the Vertex Morphing method [1] for very large shape optimization problems, where various response evaluations and multiple physics are often considered in a constrained optimization, we propose a robust modified search direction method for the optimization procedure. The solution of a general constrained gradient-based optimization problem satisfies the necessary Karush-Kuhn-Tucker (KKT) conditions [2]. There exist numerous methods to solve constrained optimization problems, which try to travel along the active constraint to find the local minimum [2][3]. This might lead to inefficiency in the optimization process for very large problems. In the proposed method, the KKT conditions are weakly imposed in each optimization step. The search direction is modified and designed to find a solution where the KKT conditions can be better fulfilled compared using the steepest descent direction. To accomplish this, the singular-value decomposition method [4] is applied to both the objective and constraint sensitivity. The results are shown first with analytical 2D problems and then the results of shape optimization problems with a large number of design variables are discussed. In order to robustly deal with complex geometries, the Vertex Morphing method is used.

Original languageEnglish
Title of host publicationProceedings of the 6th European Conference on Computational Mechanics
Subtitle of host publicationSolids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
EditorsRoger Owen, Rene de Borst, Jason Reese, Chris Pearce
PublisherInternational Centre for Numerical Methods in Engineering, CIMNE
Pages3236-3247
Number of pages12
ISBN (Electronic)9788494731167
StatePublished - 2020
Event6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 - Glasgow, United Kingdom
Duration: 11 Jun 201815 Jun 2018

Publication series

NameProceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018

Conference

Conference6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018
Country/TerritoryUnited Kingdom
CityGlasgow
Period11/06/1815/06/18

Keywords

  • Gradient-based constrained optimization
  • Karush-Kuhn-Tucker conditions
  • Shape optimization
  • Singular-value decomposition
  • Vertex Morphing

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