Semidefinite Programming via Generalized Proximal Point Algorithm

Abstract

I am grateful to my advisor Álvaro Veiga and the professors Alexandre Street and Carlos Kubrusly for their excellent technical assistance and inspiring lectures. I would like to express my gratitude to all members of LAMPS (Laboratory of Applied Mathematical Programming and Statistics) for the daily support and fruitful discussions. I would like to acknowledge the collaboration with Joaquim Garcia, which was essential to the development of this work. A special thanks to Thuener Silva for the support regarding the software development of the SDP solver. Since all code used in this work was developed in the Julia language, I would like to thank all developers involved in this open source project. In particular, I would like to acknowledge the developers of the package JuMP. The use of the domain-specific modeling language for mathematical optimization, JuMP, was fundamental for the development of this work. A special thanks to Benoît Legat for helping with ProxSDP's MOI interface. Finally, I would also like to thank the Brazilian agency CNPq and PUC-Rio university for financial support.