User:Jzeman: Difference between revisions

From Wiki @ Department of mechanics
Jump to navigation Jump to search
m (Added abstract for Michal Stingl's talk (because there is no sandbox))
Tag: Reverted
m (Replaced content with "=== Jan Zeman === * [http://mech.fsv.cvut.cz/~zemanj/ Personal page] * [https://mech.fsv.cvut.cz/web/people.php?id=60 Department page]")
Tags: Replaced Manual revert
 
Line 3: Line 3:
* [http://mech.fsv.cvut.cz/~zemanj/ Personal page]
* [http://mech.fsv.cvut.cz/~zemanj/ Personal page]
* [https://mech.fsv.cvut.cz/web/people.php?id=60 Department page]
* [https://mech.fsv.cvut.cz/web/people.php?id=60 Department page]
Design Optimization via the Continuous Stochastic Gradient Method
M. Stingl, L.Pflug, A. Uihlein
We consider large scale optimization problems with objective functions or constraints depending on random or distributed parameters. Important examples are problems, in which expected properties are minimized or problems subject to chance constraints. Here, standard deterministic optimization approaches rely on a discretization of the appearing integrals. However, the underlying quadrature rule can introduce artificial local minima, resulting in an overall poor performance of the optimizer. Since circumventing this effect severely increases the computational cost, stochastic gradient type methods have gained popularity over the years, most recently also for the solution of topology optimization problems. However, standard schemes from literature are typically limited to expected loss functions and still require many iterations. This implies that a lot of expensive state problems have to be solved. Thus, we present the continuous stochastic gradient method (CSG), which provides an efficient hybrid approach, without these limitations. In CSG, samples calculated in previous iterations are collected in an optimal linear combination to obtain an approximation to the full gradient and objective function value. It can be shown that the approximation error for both quantities vanishes during the optimization process. Therefore, CSG inherits many convergence properties known from full gradient methods, like convergence for constant step sizes. Moreover, the approximation idea in CSG is not limited to simple gradient schemes but can be combined with more elaborated sequential programming techniques. As an example, the combination with the well-known MMA-scheme is shown. After presenting the main theoretical properties of CSG, its efficiency is demonstrated for applications from elasticity and/or nano-particle optics.

Latest revision as of 22:43, 19 September 2024

Jan Zeman

Retrieved from "https://mech.fsv.cvut.cz/wiki/index.php?title=User:Jzeman&oldid=5655"