Global saddle points of nonlinear augmented Lagrangian functions

Changyu Wang, Qian Liu () and Biao Qu
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Changyu Wang: Qufu Normal University
Qian Liu: Shandong Normal University
Biao Qu: Qufu Normal University

Journal of Global Optimization, 2017, vol. 68, issue 1, No 6, 125-146

Abstract: Abstract We notice that the results for the existence of global (local) saddle points of augmented Lagrangian functions in the literature were only sufficient conditions of some special types of augmented Lagrangian. In this paper, we introduce a general class of nonlinear augmented Lagrangian functions for constrained optimization problem. In two different cases, we present sufficient and necessary conditions for the existence of global saddle points. Moreover, as corollaries of the two results above, we not only obtain sufficient and necessary conditions for the existence of global saddle points of some special types of augmented Lagrangian functions mentioned in the literature, but also give some weaker sufficient conditions than the ones in the literature. Compared with our recent work (Wang et al. in Math Oper Res 38:740–760, 2013), the nonlinear augmented Lagrangian functions in this paper are more general and the results in this paper are original. We show that some examples (such as improved barrier augmented Lagrangian) satisfy the assumptions of this paper, but not available in Wang et al. (2013).

Keywords: Dual problem for nonlinear programming; Nonlinear augmented Lagrangian function; Global saddle point; Sufficient and necessary conditions for the existence (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-016-0456-y

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