Breaking the Barrier for Tractable Global Optimization of Continuous Problems in Large Scale Data Science

In many applications of Data Science such as Image Processing, Computer Vision, Machine Learning, or Statistics the
tremendous dimensionality (even infinite for some instances), the rapidly growing data size, and the natural need to
model these problems as non-smooth and non-convex optimization problems still renders global optimization of them
intractable. This desire is significantly amplified by the prospective success of incorporating parametrized classical
regularization based models such as (continuous-valued) graphical models or variational methods into Deep Learning
models, which already now achieve state-of-the-art performance in several applications.

TRAGO aims for tractability by a paradigm shift in the design of optimization algorithms for non-convex and non-smooth continuous optimization problems, which is inspired from discrete optimization perspective. Although there has been significant progress in the area of structured non-convex (and non-smooth) optimization in recent years, most algorithms content themselves with finding stationary points instead of (approximating) a global minimizer. In contrast, TRAGO will break the barrier for tractable global optimization of continuous problems in large scale Data Science applications by theoretically and computationally investigating the optimal trade-off between gaining important properties for efficient optimization and paying for a higher dimensionality.

We will target flagship applications in Data Science which are more ambitious and far larger scale than typical
settings where these optimization problems are currently used. The work program will develop sound mathematical
and computational tools whose power will be demonstrated in several examples in Machine Learning problems such
as Graphical Models or Regularized Risk Minimization, Inverse and Variational Problems in Signal/Image Processing
and Computer Vision, and Bilevel Optimization in Data Science.

Funded by the German Research Foundation (DFG Grant OC 150/7-1).

Open Positions: We have several open PhD and PostDoc positions for this project. Applications are welcome from now on. If you are interested, send an eMail to P. Ochs (ochs@math.uni-saarland.de) and include your CV as well as a letter describing your interest and proficiency in the field.