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<p>In this paper, we consider the continuous relaxation reformulation of <i>sparsity-constrained optimization problems</i>. Based on the structure of the relaxation problem, a special <i>partially augmented Lagrangian method</i> is proposed. Unlike the classical approach, this algorithm preserves complementarity-type constraints in the augmented Lagrangian subproblems. Under mild conditions that do not depend on <i>constraint qualification</i> and do not require the multiplier sequence to be bounded, we prove that the arbitrary feasible limit point of the algorithm is <i>sparse constraints positive complementary approximately Mordukhovich stationary</i>, which is currently the strongest approximate stationary point for <i>sparsity-constrained optimization problems</i>.</p>

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Convergence of a special partially augmented Lagrangian algorithm for sparsity-constrained optimization problems

  • 期刊论文

  • 发表日期：

    2025年1月7日

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  • Menglong Xue,
  • Liping Pang

摘要

In this paper, we consider the continuous relaxation reformulation of sparsity-constrained optimization problems. Based on the structure of the relaxation problem, a special partially augmented Lagrangian method is proposed. Unlike the classical approach, this algorithm preserves complementarity-type constraints in the augmented Lagrangian subproblems. Under mild conditions that do not depend on constraint qualification and do not require the multiplier sequence to be bounded, we prove that the arbitrary feasible limit point of the algorithm is sparse constraints positive complementary approximately Mordukhovich stationary, which is currently the strongest approximate stationary point for sparsity-constrained optimization problems.