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 pr...
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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.
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