On necessity of L-stationarity in Nonlinear Optimization with a Sparsity Constraint

Authors
Abbas Khademi
Majid Soleimani-damaneh
10.52547/mmr.6.3.387
Abstract
In this paper, we investigate a necessary optimality condition for a specific problem in nonlinear programming, called sparsity constrained problem. This model involves minimizing a continuously differentiable function over a sparsity constraint. We show that L-stationarity is necessary for optimality in sparsity constrained problems in general. This important property has been proved in the literature under Lipschitzness of the gradient mapping../files/site1/files/61/6(1).pdf
Keywords
Nonlinear programming
Sparsity constrained problems
L-stationarity
Optimality condition
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Mathematical Research
Volume 6, Issue 3 - Serial Number 14
Autumn 2020
Pages 387-392