A Henig conical regularization approach for circumventing the Slater conundrum in linearly $\ell_{+}^{p}$-constrained least squares problems
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Abstract
In this paper, we study a linearly p + -constrained least-squares problem. We develop the Henig conical regularization approach as a unified framework to deal with the lack of Slater-type constraint qualification. We establish some stability estimates for the regularized problems. For the separable case, p [1, ), we provide an explicit characterization of the Henig dilating cones associated with p + and the associated regularized KKT systems. For the non-separable case + , we give a condition which ensures that the solution of the least-squares problem can be approximated by regularized solutions whose dual solutions do not contain any finitely additive singular part.
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