The Rate of Convergence of a NLM Based on F-B NCP for Constrained Optimization Problems Without Strict Complementarity

Indexed by:Journal Papers

Journal:ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH

Included Journals:SCIE、EI、Scopus

Volume:32

Issue:3

ISSN No.:0217-5959

Key Words:Nonlinear Lagrangian method; constrained optimization problems; penalty parameter; rate of convergence

Abstract:It is well-known that the linear rate of convergence can be established for the classical augmented Lagrangian method for constrained optimization problems without strict complementarity. Whether this result is still valid for other nonlinear Lagrangian methods (NLM) is an interesting problem. This paper proposes a nonlinear Lagrangian function based on Fischer-Burmeister (F-B) nonlinear complimentarity problem (NCP) function for constrained optimization problems. The rate of convergence of this NLM is analyzed under the linear independent constraint qualification and the strong second order sufficient condition without strict complementarity when subproblems are assumed to be solved exactly and inexactly, respectively. Interestingly, it is demonstrated that the Lagrange multipliers associating with inactive inequality constraints at the local minimum point converge to zeros superlinearly. Several illustrative examples are reported to show the behavior of the NLM.

Date of Publication:2015-06-01