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Canonical duality-triality is a breakthrough methodological theory, which canbe used not only for modeling complex systems within a unified framework, butalso for solving a wide class of challenging problems from real-worldapplications. This paper presents a brief review on this theory, itsphilosophical origin, physics foundation, and mathematical statements in bothfinite and infinite dimensional spaces, with emphasizing on its role forbridging the gap between nonconvex analysis/mechanics and global optimization.Special attentions are paid on unified understanding the fundamentaldifficulties in large deformation mechanics, bifurcation/chaos in nonlinearscience, and the NP-hard problems in global optimization, as well as thetheorems, methods, and algorithms for solving these challenging problems.Misunderstandings and confusions on some basic concepts, such as objectivity,nonlinearity, Lagrangian, and generalized convexities are discussed andclassified. Breakthrough from recent challenges and conceptual mistakes by M.Voisei, C. Zalinescu and his co-worker are addressed. Some open problems andfuture works in global optimization and nonconvex mechanics are proposed.

Canonical Duality-Triality Theory: Bridge Between Nonconvex Analysis/Mechanics and Global Optimization in Complex Systems