On Constrained Optimization Problems Solved Using the Canonical Duality Theory
D.Y. Gao together with some of his collaborators applied his Canonical duality theory (CDT) for solving a class of constrained optimization problems. Unfortunately, in several papers on this subject there are unclear statements, not convincing proofs, or even false results. It is our aim in this work to study rigorously this class of constrained optimization problems in finite dimensional spaces and to point out several false results published in the last ten years.
- 1.Rockafellar, R. T.: Convex Analysis. Princeton University Press, Princeton, N.J. (1972)Google Scholar
- 2.Zălinescu, C.: On quadratic optimization problems and canonical duality theory. arXiv:1809.09032 (2018)
- 3.Zălinescu, C.: On unconstrained optimization problems solved using CDT and triality theory. arXiv:1810.09009 (2018)
- 4.Ruan, N., Gao, D.Y.: Canonical duality theory for solving nonconvex/discrete constrained global optimization problems. In: Gao, D.Y., Latorre, V., Ruan, N. (eds.) Canonical Duality Theory. Advances in Mechanics and Mathematics, vol. 37, pp. 187–201. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-58017-3_9Google Scholar