Contributed Session Wed.3.MA 004

Wednesday, 15:15 - 16:45 h, Room: MA 004

Cluster 20: Robust optimization [...]

Applications of robust optimization V

 

Chair: Adrian Sichau

 

 

Wednesday, 15:15 - 15:40 h, Room: MA 004, Talk 1

Akiko Takeda
Robust optimization-based classification method

Coauthors: Takafumi Kanamori, Hiroyuki Mitsugi

 

Abstract:
The goal of binary classification is to predict the class (e.g., +1 or -1) to which new observations belong, where the identity of the class is unknown, on the basis of a training set of data containing observations whose class is known. A wide variety of machine learning algorithms such as support vector machine (SVM), minimax probability machine (MPM), Fisher discriminant analysis (FDA), exist for binary classification. The purpose of this paper is to provide a unified classification model that includes the above models through a robust optimization approach. This unified model has several benefits. One is that the extensions and improvements intended for SVM become applicable to MPM and FDA, and vice versa. Another benefit is to provide theoretical results to above learning methods at once by dealing with the unified model. We also propose a non-convex optimization algorithm that can be applied to non-convex variants of existing learning methods and show promising numerical results.

 

 

Wednesday, 15:45 - 16:10 h, Room: MA 004, Talk 2

Adrian Sichau
Shape optimization under uncertainty employing a second order approximation for the robust counterpart

Coauthor: Stefan Ulbrich

 

Abstract:
We present a second order approximation for the robust counterpart of general uncertain NLP with state equation given by a PDE. We show how the approximated worst-case functions, which are the essential part of the approximated robust counterpart, can be formulated as trust-region problems that can be solved efficiently. Also, the gradients of the approximated worst-case functions can be computed efficiently combining a sensitivity and an adjoint approach. However, there might be points where these functions are nondifferentiable. Hence, we introduce an equivalent formulation of the approximated robust counterpart (as MPEC), in which the objective and all constraints are differentiable. This formulation can further be extended to model the presence of actuators that are capable of applying forces to a structure in order to counteract the effects of uncertainty. The method is applied to shape optimization in structural mechanics to obtain optimal solutions that are robust with respect to uncertainty in acting forces and material parameters. Numerical results are presented.

 

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