@inproceedings{a96e00d41c61444aba0588122559974a,
title = "A modified search direction method with weakly imposed Karush-Kuhn-Tucker conditions for gradient based constraint optimization for very large problems",
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.",
keywords = "Gradient-based constrained optimization, Karush-Kuhn-Tucker conditions, Shape optimization, Singular-value decomposition, Vertex Morphing",
author = "Long Chen and Armin Geiser and Roland W{\"u}chner and Bletzinger, {Kai Uwe}",
note = "Publisher Copyright: copyright {\textcopyright} Crown copyright (2018).All right reserved.; 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 ; Conference date: 11-06-2018 Through 15-06-2018",
year = "2020",
language = "English",
series = "Proceedings 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",
publisher = "International Centre for Numerical Methods in Engineering, CIMNE",
pages = "3236--3247",
editor = "Roger Owen and {de Borst}, Rene and Jason Reese and Chris Pearce",
booktitle = "Proceedings of the 6th European Conference on Computational Mechanics",
}