Advances in Polynomial Optimization

Polynomial optimization has a wide range of practical applications in fields such as optimal control, energy and water networks, facility location, management science, and finance. It also generalizes relevant optimization problems thoroughly studied in the literature, such as mixed-binary linear optimization, quadratic optimization, and complementarity problems. As finding globally optimal solutions is an extremely challenging task, the development of efficient techniques for solving polynomial optimization problems is of particular relevance. In this thesis we provide a detailed study of different techniques to solve this kind of problems and we introduce some nobel approaches in this field, including the use of statistical learning techniques. Furthermore, we also present a practical application of polynomial optimization to finance and more specifically, portfolio design

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

QoS constrained robust MIMO transceiver design under unknown interference

We study the robust transceiver optimization in multiple-input multiple-output (MIMO) systems aiming at minimizing transmit power under probabilistic quality-of-service (QoS) requirements. Owing to the unknown distributed interference, the channel estimation error can be arbitrary distributed. Under this situation, the QoS requirements should account for the worst-case channel estimation error distribution. While directly finding the worst-case distribution is challenging, two methods are proposed to solve the robust transceiver design problem. One is based on the Chebyshev inequality, the other is based on a novel duality method. Simulation results show that the QoS requirement is satisfied by both proposed algorithms. Furthermore, among the two proposed methods, the duality method shows a superior performance in transmit power, while the Chebyshev method demonstrates a lower computational complexity. © 2012 IEEE.published_or_final_versio