- Title
- Canonical duality-triality theory: Bridge between nonconvex analysis/mechanics and global optimization in complex system
- Creator
- Gao, David; Ruan, Ning; Latorre, Vittorio
- Date
- 2017
- Type
- Text; Book chapter
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/179293
- Identifier
- vital:15566
- Identifier
- https://link.springer.com/chapter/10.1007/978-3-319-58017-3_1
- Identifier
- ISBN:978-3-319-58016-6
- Abstract
- Canonical duality-triality is a breakthrough methodological theory, which can be used not only for modeling complex systems within a unified framework, but also for solving a wide class of challenging problems from real-world applications. This paper presents a brief review on this theory, its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. Particular emphasis is placed on its role for bridging the gap between nonconvex analysis/mechanics and global optimization . Special attentions are paid on unified understanding the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization, as well as the theorems, methods, and algorithms for solving these challenging problems. Misunderstandings and confusion on some basic concepts, such as objectivity , nonlinearity, Lagrangian , and generalized convexities are discussed and classified. Breakthrough from recent challenges and conceptual mistakes by M. Voisei, C. Z
- Publisher
- Springer
- Relation
- Canonical duality theory: Unified methodology for multidisciplinary study Chapter 1 p. 1-47
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- © Springer International Publishing AG 2017
- Subject
- Mathematics; Mathematical optimization
- Reviewed
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