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Implementation of a semidefinite optimization solver in the Julia programming language

Kwasniewicz, Tomasz
(2021)

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Kwasniewicz_21071600_2021.pdf
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Details

Supervisors
Glineur, François
Faculty
Ecole polytechnique de Louvain
Degree label
Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée
Abstract
Semidefinite programming has become a major research topic in optimization, finding applications in multiple domains. This surge of interest sparked the need for efficient solution methods and user-friendly software in order to deploy semidefinite programming in practice. At the same time, the Julia programming language introduced in 2012 became a major platform for developing optimization software. This report focuses on presenting the implementation of an interior-point solver for semidefinite programming written entirely in Julia. The solver implements a Mehrotra-type predictor-corrector interior-point method. In order to assess its performance, several benchmarks are completed. These benchmarks are performed on a widely used problem set (SDPLIB) and several interior-point as well as first-order solvers are tested. The obtained results show that this newly implemented solver can achieve a decent performance and be even slightly faster than some well-established solvers for some problems. Concepts related to this report are: semidefinite programming, conic optimization, Julia programming language.