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http://hdl.handle.net/10397/5880
Title: | A nonlinear Lagrangian approach to constrained optimization problems | Authors: | Yang, XQ Huang, XX |
Issue Date: | 2001 | Source: | SIAM journal on optimization, 2001, v. 11, no. 4, p. 1119-1144 | Abstract: | In this paper we study nonlinear Lagrangian functions for constrained optimization problems which are, in general, nonlinear with respect to the objective function. We establish an equivalence between two types of zero duality gap properties, which are described using augmented Lagrangian dual functions and nonlinear Lagrangian dual functions, respectively. Furthermore, we show the existence of a path of optimal solutions generated by nonlinear Lagrangian problems and show its convergence toward the optimal set of the original problem. We analyze the convergence of several classes of nonlinear Lagrangian problems in terms of their first and second order necessary optimality conditions. | Keywords: | Augmented Lagrangian Nonlinear Lagrangian Zero duality gap Optimal path Necessary optimality condition Smooth approximate variational principle |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM Journal on optimization | ISSN: | 1052-6234 | EISSN: | 1095-7189 | DOI: | 10.1137/S1052623400371806 | Rights: | © 2001 Society for Industrial and Applied Mathematics |
Appears in Collections: | Journal/Magazine Article |
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