I work with computational mathematics, mostly with nonlinear optimization. Some topics of my interest:

  • Unconstrained minimization methods;
  • Box-constrained minimization;
  • Large-scale methods;
  • Matrix-Free Optimization;
  • Integer and Linear Programming;
  • Computational Linear Algebra;
  • Julia language;
  • Comparison and benchmarking of optimization methods;
  • Reproducible science;
  • Free open source tools.

I have interest in, or am working at, the following projects. If you are a student looking for a research topic, this is a good start.

Perprof-py: A Python tool for generating Performance Profiles

Follow up to this work. Some topics:

  • Web interface;
  • v2.0.

Simplex Implementation in Julia

The objective of this project is implement an efficient Simplex algorithm in Julia. There are many steps in this project, a few are listed below:

  • Basic Simplex;
  • Bounded Simplex;
  • Dual Simplex;
  • JuMP integration;
  • Basis factorization update;
  • Pre-processing;
  • Integer problem implementation.

Framework for Nonlinear Optimization in Julia

This is a joint work with Dominique Orban, reasonably advanced, but with some space for work. We are creating a working environment to develop optimization methods in Julia. This project includes:

  • Creation and use of nonlinear models with an unified API;
  • CUTEst access inside Julia;
  • Linear operators efficiently;
  • Krylov methods;
  • Tools for methods comparison;

To know more, check the organization JuliaSmoothOptimizers.

  • Keywords: Nonlinear Optimization, Julia, CUTEst

Reproducible Science and Free Open Source Software

When the next “best optimization algorithm ever” comes around, I want to be able to verify the claim. This is only possible through reproducible science. The data and steps that describe a research should be available to the peers. Some easy steps can be taken to improve the reproducibility and availability of a research project, and I think believe this should be of greater concern that it is. Furthermore, when dealing with reproducible science, I believe that free software should be considered whenever possible. The reproducibility of a project is limited when using proprietary software.

  • Keywords: Reproducible Science, Open Science, Open Source, Free Software

Computational Tools for Researchers and Software Carpentry

In the spirit of good and reproducible science, some tools are very important, and useful, for a researchers. Despite the field, a researcher may find that some tasks would be better left for the computer, such as renaming thousands of files.

One organization that helps in that endeavor is Software Carpentry. Software Carpentry provides researchers with a short introduction class to several of these tools. Whenever possible, instructors are taken from the same field as that of the researcher.

Some noteworthy tools are Git, LaTeX, Bash, Python, Julia and Markdown.

  • Keywords: Computational Tools, Software Carpentry