Jacob Aguirre

I am a 4th year Operations Research PhD Candidate at the H. Milton Stewart School of Industrial and Systems Engineering (ISyE) at Georgia Institute of Technology. I am grateful to be advised by Professors Anton J. Kleywegt, Renato D.C. Monteiro, and Dmitrii Ostrovskii. My research interests lie in the area of continuous optimization and complexity of algorithms. More specifically, I am interested in the theory, complexity analysis, and implementation of algorithms for solving large-scale optimization programs.

Bicriteria Traffic Assignment

Published: 2026/11/10

Network Optimization, Nonsmooth Optimization, Transportation bicriteria traffic assignment, heterogeneous value of time, nonsmooth convex optimization, parametric shortest path, Wardrop equilibrium

The classical traffic assignment problem determines the equilibrium flows on a congested network with many infinitesimal users who choose paths to minimize their own travel times. Travelers care about cost (including tolls) as well as time, and different travelers put different weights on these two criteria. We study a bicriteria traffic assignment problem in which … Read more

Entropy-Smooth Convex Optimization Cannot Be Accelerated

Published: 2026/07/30

Convex and Nonsmooth Optimization, Convex Optimization, Optimization in Data Science complexity, convex optimization, nonlinear programming

We prove an $\Omega(L/T)$ lower bound for the convergence rate of minimization in the class of functions that are convex and $L$-smooth relative to negative entropy on the standard $d$-simplex, valid for every first-order method when $d = \Omega(T^2)$. In particular, this shows that mirror descent is optimal up to a logarithmic factor in this … Read more

A user manual for cuHALLaR: A GPU accelerated low-rank semidefinite programming Solver

Published: 2025/08/21

Nonlinear Optimization, Optimization Software and Modeling Systems, Semi-definite Programming augmented Lagrangian, Burer-Monteiro factorization, frank-wolfe, gpu, large scale semidefinite programming, low-rank factorization, SDP solver

We present a Julia-based interface to the precompiled HALLaR and cuHALLaR binaries for large-scale semidefinite programs (SDPs). Both solvers are established as fast and numerically stable, and accept problem data in formats compatible with SDPA and a new enhanced data format taking advantage of Hybrid Sparse Low-Rank (HSLR) structure. The interface allows users to load … Read more

cuHALLaR: A GPU accelerated low-rank augmented Lagrangian method for large-scale semidefinite programming

Published: 2025/05/19, Updated: 2026/11/10

Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems augmented Lagrangian, conic and semidefinite programming, convex and nonconvex optimization, frank-wolfe, gpu, low-rank factorization

This paper presents cuHALLaR, a GPU-accelerated solver with an explicit trace constraint $\mathrm{Tr}(X)\leq \tau^2$, where $\tau$ is supplied as part of the problem data. The solver is a Julia-based implementation of the hybrid low-rank augmented Lagrangian method, HALLaR, previously proposed by three of the authors. It exploits massive parallelism by performing all core operator evaluations, … Read more