This book offers a unique pathway to methods of parallel optimization by introducing parallel computing ideas and techniques into both optimization theory, and into some numerical algorithms for large-scale optimization problems. The presentation is based on the recent understanding that rigorous mathematical analysis of algorithms, parallel computing techniques, and "hands-on" experimental work on real-world problems must go hand in hand in order to achieve the greatest advantage from novel parallel computing architectures. The three parts of the book thus bring together relevant theory, careful study of algorithms, and modelling of significant real world problems. The problem domains include: image reconstruction, radiation therapy treatment planning, transportation problems, portfolilo management, and matrix estimation. This text can be used both as a reference for researchers and as a text for advanced graduate courses.

Brings together 27 state-of-the-art research and review papers by leading experts and practitioners in mathematical methods in biomedical imaging, in intensity-modulated radiation therapy (IMRT) and in optimisation and inverse problems. These papers were presented at the Huangguoshu International Interdisciplinary Conference on Biomedical Mathematics-Promising Directions in Imaging, Therapy Planning, and Inverse Problems November 3-9, 2008 in China. The emphasis is on trying to discover relations and connections between these fields that will enhance progress in each of them. As this volume shows, applicable mathematical work in these fields goes hand-in-hand with real-world applications and the mutual ""technology transfers"" between them leads to further progress. The topics covered here include mathematical aspects and practical problems in current major and emerging technologies in diagnostic and therapeutic medicine and biology research. The contributed work signifies the interdisciplinary cooperation between mathematicians and scientists from medical physics, engineering, clinical medicine, and biology that leads to mathematically based better solutions of practical problems in biomedical imaging and IMRT.