Taming Nonconvexity in Solving High-Dimensional Nonlinear Systems of Equations
Abstract
This research project aims to develop foundational theory and efficient algorithms that allow to solve high-dimensional nonlinear systems of equations in a time-critical, robust, and model-insensitive manner. This is a key enabler of efficient extraction of meaningful information and actionable intelligence from complex data sources in various modern data science applications. At the core of such challenges is the nonconvexity issue: a diverse array of such problems can naturally be formulated as nonconvex optimization problems. However, the dramatically increased dimensionality of data requires one to solve large-scale nonconvex optimization problems, which are computationally infeasible in general. Focusing on the design and analysis of problem-specific nonconvex optimization algorithms, an overall goal is to design a new suite of nonconvex optimization methods that that possess both statistical and computational guarantees when accommodating the ever-increasing dimensionality of the problems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 20, 2023
- Accession Number
- AD1230490
Entities
People
- Yuxin Chen
Organizations
- Princeton University