Existence of augmented Lagrange multipliers for cone constrained optimization problems

Authors:
Yu Ying Zhou;Jin Chuan Zhou;Xiao Qi Yang
Affiliations:
Department of Mathematics, Soochow University, Suzhou, China 215006;Department of Mathematics, School of Science, Shandong University of Technology, Zibo, China 255049;Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China
Venue:
Journal of Global Optimization
Year:
2014

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Abstract

In this paper, by using an augmented Lagrangian approach, we obtain several sufficient conditions for the existence of augmented Lagrange multipliers of a cone constrained optimization problem in Banach spaces, where the corresponding augmenting function is assumed to have a valley at zero. Furthermore, we deal with the relationship of saddle points, augmented Lagrange multipliers, and zero duality gap property between the cone constrained optimization problem and its augmented Lagrangian dual problem.