Smoothing augmented Lagrangian method for nonsmooth constrained optimization problems

Indexed by:Journal Papers

Journal:JOURNAL OF GLOBAL OPTIMIZATION

Included Journals:SCIE、EI、Scopus

Volume:62

Issue:4,SI

Page Number:675-694

ISSN No.:0925-5001

Key Words:Nonsmooth optimization; Constrained optimization; Smoothing function; Augmented Lagrangian method; Constraint qualification; Bilevel program

Abstract:In this paper, we propose a smoothing augmented Lagrangian method for finding a stationary point of a nonsmooth and nonconvex optimization problem. We show that any accumulation point of the iteration sequence generated by the algorithm is a stationary point provided that the penalty parameters are bounded. Furthermore, we show that a weak version of the generalized Mangasarian Fromovitz constraint qualification (GMFCQ) at the accumulation point is a sufficient condition for the boundedness of the penalty parameters. Since the weak GMFCQ may be strictly weaker than the GMFCQ, our algorithm is applicable for an optimization problem for which the GMFCQ does not hold. Numerical experiments show that the algorithm is efficient for finding stationary points of general nonsmooth and nonconvex optimization problems, including the bilevel program which will never satisfy the GMFCQ.

Date of Publication:2015-08-01