This book gathers the peer-reviewed proceedings of the 14th Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics, BGSIAM''19, held in Sofia, Bulgaria. The general theme of BGSIAM''19 was industrial and applied mathematics with particular focus on mathematical physics, numerical analysis, high-performance computing, optimization and control, mathematical biology, stochastic modeling, machine learning, digitization and imaging, and advanced computing in environmental, biomedical, and engineering applications.