Unconstrained Convex Optimization using Gradient Descent

Author: Vishvas Ranjan, UM‑DAE Centre for Excellence in Basic Sciences, Mumbai, India Supervisor: Dr. Sherry Sarkar, Carnegie Mellon University, Pittsburgh, USA

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Project Context

This repository contains the deliverables for the summer research project conducted under the Polymath Jr. Research Experience for Undergraduates (ReU) program, within the "Surveys in Theoretical Computer Science" group. The work was also presented at the Joint Mathematics Meetings (JMM) 2024, San Francisco (January 3–6, 2024), hosted by the American Mathematical Society.

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Contents

1. Project_Report.pdf A detailed written report covering:

   • Background on unconstrained convex optimization.
   • Derivation and analysis of the gradient descent algorithm.
   • Convergence proofs under various smoothness and convexity assumptions.
   • Numerical experiments and performance plots.

2. Presentation_PolymathJr_ReU.pdf Slides presented during the Polymath Jr ReU summer program. Highlights include:

   • Motivation and problem statement.
   • Algorithmic framework and theoretical results.
   • Sample experiments and key takeaways.

3. Presentation_JMM2024.pdf Slides for the Joint Mathematics Meetings 2024:

   • Refined overview of results.
   • Extended discussion on practical implications.

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Acknowledgements

• Polymath Jr ReU Organizers for guidance and mentorship.
• American Mathematical Society for hosting JMM 2024.
• National Board for Higher Mathematics (NBHM), INDIA and National Science Foundation (NSF), USA for providing travel grants.
• Dr. Sherry Sarkar, Prof. Steven Miller and Prof. Adam Sheffer for supervision and insightful discussions.

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