Some Results on Augmented Lagrangians in Constrained Global Optimization via Image Space Analysis

Hezhi Luo (), Huixian Wu () and Jianzhen Liu ()
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Hezhi Luo: Zhejiang University of Technology
Huixian Wu: Hangzhou Dianzi University
Jianzhen Liu: Hangzhou Dianzi University

Journal of Optimization Theory and Applications, 2013, vol. 159, issue 2, No 4, 360-385

Abstract: Abstract The aim of this paper is to present some results for the augmented Lagrangian function in the context of constrained global optimization by means of the image space analysis. It is first shown that a saddle point condition for the augmented Lagrangian function is equivalent to the existence of a regular nonlinear separation in the image space. Local and global sufficient optimality conditions for the exact augmented Lagrangian function are then investigated by means of second-order analysis in the image space. Local optimality result for this function is established under second-order sufficiency conditions in the image space. Global optimality result is further obtained under additional assumptions. Finally, it is proved that the exact augmented Lagrangian method converges to a global solution–Lagrange multiplier pair of the original problem under mild conditions.

Keywords: Constrained global optimization; Image space analysis; Nonlinear separation; Augmented Lagrangian function; Saddle point (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-013-0358-9

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