23 citations · 37 across the 15 of their papers we have counts for
4 papers · 1 filter
Shape optimization in with geometric constraints: a study in distributed-memory systems
Philip J. Herbert, Jose A. Pinzon Escobar, Martin Siebenborn
In this paper we present a shape optimization scheme which utilizes the alternating direction method of multipliers (ADMM) to approximate a direction of steepest descent in $W^{1,\…
The Stochastic Steepest Descent Method for Robust Optimization in Banach Spaces
Neil K. Chada, Philip J. Herbert
Stochastic gradient methods have been a popular and powerful choice of optimization methods, aimed at minimizing functions. Their advantage lies in the fact that that one approxima…
Shape Optimisation with : A connection between the steepest descent and Optimal Transport
Philip J. Herbert
In this work, we discuss the task of finding a direction of optimal descent for problems in Shape Optimisation and its relation to the dual problem in Optimal Transport. This link…
PDE constrained shape optimisation with first-order and Newton-type methods in the topology
Klaus Deckelnick, Philip J. Herbert, Michael Hinze
We present a general shape optimisation framework based on the method of mappings in the topology. We propose steepest descent and Newton-like minimisation algorithm…