Systematic and computer-aided performance certification for numerical optimization

Introduction

Numerical optimization is a fundamental tool with a growing impact in many disciplines from science to industry. Many of its successes are due to theoretical advances, which are key to developing trust in numerical algorithms. While trust is non-negotiable in many applications, the complexity level of modern and future problems makes it very hard for theory to keep up with efficient proposals.

Theory vs. Practice

Arguably worse, while both theory and experimental practice are key to the field, their respective recommendations often conflict with each other and the gap between theory and practice gets embarrassingly large.

Project Objective

The main objective of this proposal is to push forward the theoretical foundations of algorithmic optimization to drastically reduce the gap between fundamental theoretical understanding and practical scenarios.

Approach

To achieve this, we will develop principled and systematic approaches to algorithmic analyses, as well as computer-aided performance certification tools.

1. My recent works show that such techniques already allow going far beyond the surprisingly few classical templates for algorithmic analysis.
2. However, they currently have very limited applicability beyond simple scenarios.
3. We will largely broaden the techniques to develop and study modern algorithms with working guarantees that can:
   • Scale to unprecedented problem and data sizes,
   • Adapt to common problem structures, and
   • Be deployed on modern massively parallel computing environments.

Impact

On the way, this project will allow for simplified certification and validation of existing theory, an absolute necessity in this era of massive scientific production.

Expected Outcomes

Outcomes of CASPER will include:

• Symbolical and numerical algorithmic certification and development tools,
• Algorithms with unprecedented working guarantees.

The tools will be released as open-source libraries and algorithms validated on key benchmarks that include challenging machine learning and robotic tasks.