Multi-Duality and Classifications of General Systems
The quadratic canonical dual transformation method, presented in Chapter 3, can be generalized in different ways for solving general nonconvex systems. We begin with a special nonconvex variational problem with multi-well energy. Then, we present two powerful sequential dual transformations for general nonconvex systems with multi-well energy. These two methods produce two different duality theories. The classifications are discussed for general systems and a generalized tri-duality principle is presented in the central part of this section, which plays a core role in this book. Examples from discrete systems and continuum fields are listed. We end up by giving an application for nonconvex systems.
KeywordsPolar System Dual Transformation Canonical System Duality Principle Criticality Condition
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