Splitting Algorithms, Modern Operator Theory, and Applications (17w5030)


Heinz Bauschke (UBC Okanagan)

(University of South Australia)

Russell Luke (Georg-August Universität Göttingen)


The Casa Matemática Oaxaca (CMO) will host the "Splitting Algorithms, Modern Operator Theory, and Applications " workshop from September 17th to September 22nd, 2017.

The most urgent problems we face today - global warming or economic crises may come to mind - are too large and too complex to solve through one monolithic action. Like a Sudoku puzzle, we start with something that we can do, something that is manageable - turn down the thermostat, lower interest rates - and hope that the accumulation of positive moves will lead, eventually, to a solution. In some cases there is solid mathematical theory to guarantee when and how decompositions of problems into simpler parts result in procedures, or courses of action, that are guaranteed to lead to a solution. Understanding the behaviour of these procedures, otherwise known as splitting methods, in increasingly complex environments - when they work, how fast they work, and how close to the solution you need already to be before they will work - is the subject of monotone operator theory, and the reason for this workshop in Banff.

Leading researchers on splitting methods are meeting to make these algorithms more efficient through surveying the latest research results, exchanging ideas and techniques, and exploring new areas of applications, ranging from road design, through astronomy to solving Sudoku puzzles and similar discrete optimization problems. The expected results catalyzed through this workshop have the potential to improve industrial processes and ultimately our lives and understanding. Special focus is also given to train the next generation of scientists in this important area.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry.

The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT.