In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of admissible transformations. The focus is on the choice of the set of transformations, which we motivate from a function space perspective. In order to guarantee local injectivity of the admissible transformations we enrich the optimization problem by a nonlinear constraint. The approach requires no parameter tuning for the extension equation and can naturally be combined with geometric constraints on volume and barycenter of the shape. Numerical results for drag minimization of Stokes flow are presented.
Understanding the Variance Dichotomy in Continuous Simulation Optimization: A Minimax Lower Bound Perspective
Faculty of Business for Science and Technology, School of Management, University of Science and Technology of China（中国科学技术大学管理学院）；Department of Industrial and Systems Engineering, University of Minnesota（明尼苏达大学工业与系统工程系）
Variable Aggregation-based Perspective Reformulation for Mixed-Integer Convex Optimization with Symmetry
School of Economics and Management, North China Electric Power University（华北电力大学经济与管理学院）；Thayer School of Engineering, Dartmouth College（达特茅斯学院塔克工程学院）；School of Economics and Management, University of Chinese Academy of Sciences（中国科学院大学经济与管理学院）；Department of Industrial and Systems Engineering, North Carolina State University（北卡罗来纳州立大学工业与系统工程系）
Efficient and accurate separable models for discrete material optimization: A continuous perspective
Johann Radon Institute for Computational and Applied Mathematics（约翰·拉顿计算与应用数学研究所）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）
