Efficient Homotopy Methods for Higher Order Shape Optimization: A Globalized Shape-Newton Approach and Pareto-Front Tracing

This work presents a globalized shape-Newton method that combines higher order shape optimization with homotopy (continuation) techniques to efficiently solve shape optimization problems, even when the initial design is far from the optimal solution. The authors also apply homotopy methods to multi-objective shape optimization to effectively trace the Pareto front.