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New convergence properties of the primal augmented Lagrangian method. (English) Zbl 1242.49032

Summary: New convergence properties of the proximal augmented Lagrangian method are established for a continuous nonconvex optimization problem with both equality and inequality constraints. In particular, the multiplier sequences are not required to be bounded. Different convergence results are discussed dependent on whether the iterative sequence \(\{x^k\}\) generated by algorithm is convergent or divergent. Furthermore, under certain convexity assumption, we show that every accumulation point of \(\{x^k\}\) is either a degenerate point or a KKT point of the primal problem. Numerical experiments are presented finally.

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
49M30 Other numerical methods in calculus of variations (MSC2010)
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