Abstract
This paper presents a perfect duality theory for solving nonsmooth, concave minimization problems subjected to inequality constraints. By use of the canonical dual transformation developed recently, a canonical dual problem is formulated, which is perfectly dual to the primal problem with zero duality gap. It is shown that the global minimizer and local extrema of the nonconvex problem can be identified by the triality theory discovered recently (Gao, 2000). This canonical dual form and the triality theory can be used to develop certain powerful algorithms for solving nonsmooth concave minimization problems.
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Gao, D.Y. (2006). Canonical Duality in Nonsmooth, Constrained Concave Minimization. In: Alart, P., Maisonneuve, O., Rockafellar, R.T. (eds) Nonsmooth Mechanics and Analysis. Advances in Mechanics and Mathematics, vol 12. Springer, Boston, MA. https://doi.org/10.1007/0-387-29195-4_25
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DOI: https://doi.org/10.1007/0-387-29195-4_25
Publisher Name: Springer, Boston, MA
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