Local convexification of the Lagrangian function in nonconvex optimization
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AbstractIt is well-known that a basic requirement for the development of local duality theory in nonconvex optimization is the local convexity of the Lagrangian function. This paper shot-vs how to locally convexify the Lagrangian function and thus expand the class of optimization problems to which dual methods can be applied. Specifically, we prove that, under mild assumptions, the Hessian of the Lagrangian in some transformed equivalent problem formulations becomes positive definite in a neighborhood of a local optimal point of the original problem.
All Author(s) ListLi D, Sun XL
Journal nameJournal of Optimization Theory and Applications
Volume Number104
Issue Number1
Pages109 - 120
LanguagesEnglish-United Kingdom
KeywordsLagrangian function; local convexification; local duality; nonconvex optimization; p-power formulation
Web of Science Subject CategoriesMathematics; Mathematics, Applied; MATHEMATICS, APPLIED; Operations Research & Management Science; OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Last updated on 2021-11-01 at 00:55