My research interests are in the area of continuous optimization and algorithmic complexity.

• (Major) Theory and complexity analysis: Development of efficient algorithms for large-scale linear programming, convex quadratic programming, semidefinite programming, variational inequalities, and nonlinear convex programming.
• (Minor) Computational optimization: Developing numerical codes for solving these large-scale optimization problems efficiently.

More recently, I am interested in the following areas:

• GPU Accelerated First-Order Methods
• Adaptive parameter-free methods for convex optimization
• Algorithms for Semidefinite & Copositive Programming
• Nonsmooth optimization methods, especially bundle-level and prox-bundle

Jacob M. Aguirre, Renato D.C. Monteiro, Anton J. Kleywegt. Hybrid Approaches for Large-Scale Linear Programs (Working paper)

Jacob M. Aguirre, Anton J. Kleywegt, Renato D.C. Monteiro. Efficient algorithms for Bicriteria Traffic Assignment (Working paper)

Jacob M. Aguirre, Renato D.C. Monteiro, Anton J. Kleywegt. Complexity Analysis and Implementation of an accelerated smoothing gradient method (Working paper)

Renato D.C. Monteiro and Jacob M. Aguirre. A New Memory-efficient method for Sparse Plus Low Rank Semidefinite Programming

Jacob M. Aguirre, Diego Cifuentes, Vincent Guigues, Victor Hugo Nascimento, Renato D.C. Monteiro, Arnesh Sujanani. An Accelerated Hybrid Low-Rank Augmented Lagrangian Method for Large-Scale Semidefinite Programming on GPU (Working paper)

Jacob Aguirre, Shrey Patel, Ruirui Ma. A Review of High Dimensional Nonlinear Dimension Reduction Methods Undergrad course paper