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<p>In this paper we consider an augmented Lagrangian method with general lower-level constraints, that is, where some of the constraints are penalized while others are kept as subproblem constraints. Motivated by some recent results on optimization problems on manifolds, we present a general theory of global convergence when a feasible approximate KKT point is found for the subproblems at each iteration. In particular, we formulate new constant rank constraint qualifications that do not require a constant rank assumption in a full dimensional neighborhood of the point of interest. We also formulate an appropriate quasinormality and relaxed-quasinormality conditions which guarantee boundedness of the dual sequences generated by the algorithm. These assumptions apply, in particular, to the current ALGENCAN implementation that keeps box constraints within the subproblems.</p>

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On constraint qualifications for non-relaxable sets and an augmented Lagrangian method

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月15日

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  • Roberto Andreani,
  • Gabriel Haeser,
  • Mariana da Rosa,
  • Daiana O. Santos

摘要

In this paper we consider an augmented Lagrangian method with general lower-level constraints, that is, where some of the constraints are penalized while others are kept as subproblem constraints. Motivated by some recent results on optimization problems on manifolds, we present a general theory of global convergence when a feasible approximate KKT point is found for the subproblems at each iteration. In particular, we formulate new constant rank constraint qualifications that do not require a constant rank assumption in a full dimensional neighborhood of the point of interest. We also formulate an appropriate quasinormality and relaxed-quasinormality conditions which guarantee boundedness of the dual sequences generated by the algorithm. These assumptions apply, in particular, to the current ALGENCAN implementation that keeps box constraints within the subproblems.