Aaron Zoll

About Me

I am a PhD student at The Johns Hopkins University in the department of Applied Math and Statistics. My work primarily focuses in optimization, under the supervision of Benjamin Grimmer. My work primarily focuses on the algorithm design and analysis. In particular, I work on expanding classical optimization theory to apply universally to Lipschitz functions, functions with Lipschitz gradient, and everywhere in between. Dually, my work sometimes considers functions exhibiting strong convexity, simple convexity, or anywhere in between.

Below are a few selected papers, unifying calculus results and algorithm design for a wide range of function classes. Further below, I give selections from my Desmos Gallery, a series of interactive graphs. Feel free to experiment and play; I hope these are as fun to interact with as they were to create.

Curriculum Vitae LinkedIn Desmos Gallery Email

Selected Papers

Inexactly Smooth Performance Estimation and New Optimized Gradient Methods

slides arXiv

A Universally Optimal Primal-Dual Method for Minimizing Heterogeneous Compositions
(IMA Journal of Numerical Analysis)

slides arXiv

Second Order Runge-Kutta Methods

Runga Kutta Methods are efficient and practical ways to accurately model a trajectory given information about its underlying vector field. Here we demonstrate multiple classical two-step methods, as well as the general form supplying a class of provably convergent methods. Watch how increasing the number of steps (decreasing the step size) affects the stability of the iteratively built trajectory!

Lagrange/Hermite Interpolation

Interpolation theory has many applications in data science, optimization, and machine learning. Here, you may explore polynomial interpolation through both Lagrange and Hermite basis functions, the former interpolating points and function values while the latter incorporates derivatives. Toggle between these methods and isolate individual basis polynomials to see how they sum to produce the full interpolant.

Taylor Series

Construct polynomials to approximate smooth functions using perhaps the most important results from calc II. As you increase the degree, you may notice the polynomial converge, but be wary that depending on the function, its radius of convergence may be finite.

Finite Difference Interpolation

Here you may visualize how finite difference methods approximate derivatives. Compare standard central difference formulas, or interact with custom interpolation nodes to derive general finite difference rules.

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