Smoothing augmented Lagrangian method for nonsmooth constrained optimization problems

Mengwei Xu (), Jane Ye () and Liwei Zhang ()

Journal of Global Optimization, 2015, vol. 62, issue 4, 675-694

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. Copyright Springer Science+Business Media New York 2015

Keywords: Nonsmooth optimization; Constrained optimization; Smoothing function; Augmented Lagrangian method; Constraint qualification; Bilevel program; 65K10; 90C26 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-014-0242-7

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