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内容简介:Duality is an inspiring, fundamental concept that underlies almost all natural phenomena. In mathematical science, dynamical systems, global optimization, economics, control theory, numerical methods and scientific computation, duality principles and methods are playing more and more important roles. Canonical duality theory is a newly developed, potentially powerful methodology, which can be used to solve a large class of difficult problems in mathematical analysis and optimization.
In this talk, the speaker will give a brief introduction to the canonical duality theory and its role in mathematical analysis and optimization. By using some simple but very interesting problems in global optimization, the speaker will first present a unified structure and splendid beauty in mathematical science. The traditional Lagrangian duality theory will be explained in a new way. A potentially powerful canonical dual transformation method and the associated triality theory will be introduced by using some simple examples in nonconvex optimization. He will show that by using this method, many very difficult problems can be solved in an elegant way. Applications will be illustrated by certain well-known global optimization problems. This talk should bring some fundamentally new insights into mathematical science.
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