D. R. Souza

Campinas-SP, Brazil

I am Danilo R. Souza, a mathematician (B.Sc., M.Sc., and Ph.D. in Mathematics from the Federal University of Goias - UFG) and a researcher working in Continuous Optimization, Multiobjective Optimization, and Inverse Problems.

I completed a postdoctoral position in Applied Mathematics at USP (2024), with emphasis on inverse problems. My current research is strongly connected to seismic inversion and Full Waveform Inversion (FWI), with a special interest in large-scale stochastic optimization for elastic FWI.

I also develop open source Julia software for multiobjective optimization through the Vector Optimization Group, including benchmark problems, line searches, and solvers.

Location: Campinas-SP, Brazil
Areas: Mathematical Optimization, Stochastic Optimization, Multiobjective Optimization, Derivative-Free Methods, Inverse Problems, FWI and EFWI
Applied interests: Computational geophysics, numerical methods, HPC, and multi-language pipelines (Julia/Python/C)

news

Oct 17, 2026	MultiObjectiveProblems.jl is now registered in Julia’s General registry and can be installed with `Pkg.add("MultiObjectiveProblems")`. Explore the documentation.
Oct 17, 2026	MultiObjectiveLineSearches.jl is now available as a standalone Julia package, refactored from the line searches previously included in MOSolvers.jl. Read the documentation.
May 23, 2026	Our submitted paper A Partially Derivative-Free Proximal Method for Composite Multiobjective Optimization in the Holder Setting is available on arXiv.
Sep 24, 2025	I presented Multiobjective Optimization Strategies: A Comparative Analysis Focused on Direct Vector Methods at the 13th UFPI Mathematics Conference.
May 01, 2025	I am a co-founder of VectorOptimizationGroup, a GitHub organization focused on software for multiobjective/vector optimization.

selected publications

JOTA
A quasi-Newton method with Wolfe line searches for multiobjective optimization

L. F. Prudente and D. R. Souza

Journal of Optimization Theory and Applications, Mar 2022

Abs DOI Bib PDF Code

We propose a BFGS method with Wolfe line searches for unconstrained multiobjective optimization problems. The algorithm is well defined even for general nonconvex problems. Global convergence and R-linear convergence to a Pareto optimal point are established for strongly convex problems. In the local convergence analysis, if the objective functions are locally strongly convex with Lipschitz continuous Hessians, the rate of convergence is Q-superlinear. In this respect, our method exactly mimics the classical BFGS method for single-criterion optimization.
@article{prudente2022bfgswolfe, title = {A quasi-Newton method with Wolfe line searches for multiobjective optimization}, author = {Prudente, L. F. and Souza, D. R.}, journal = {Journal of Optimization Theory and Applications}, volume = {194}, pages = {1107--1140}, year = {2022}, month = mar, doi = {10.1007/s10957-022-02072-5}, }