My research designs and analyzes scalable nonlinear optimization algorithms for decision-making problems complicated by uncertainty, limited problem information, massive dimensionality, and complex constraints. My work draws on optimization theory, linear algebra, and probability, with applications in machine learning, scientific computing, and simulation optimization.

Adaptive Methods

I develop stochastic linesearch methods that select stepsizes without problem parameters or costly tuning. We developed the Stochastic LineseArch Method (SLAM) and accelerated extensions for smooth and nonsmooth stochastic convex optimization. These methods reuse samples efficiently while retaining rigorous convergence and complexity guarantees. 

Inexact Methods

I design algorithms that reduce the cost of second-order steps through iterative linear algebra and principled inexactness. My work on ITRACE, a trust-region method, identifies implementable accuracy conditions that preserve optimal worst-case iteration and matrix-vector product complexity guarantees. 

Constrained Methods

My work develops stochastic SQP and interior-point methods that handle nonlinear constraints directly. These methods target constrained learning problems, including physics-informed neural networks, while preserving feasibility and convergence guarantees. I am also developing filter methods for optimization with deterministic bounded noise.