## Lidia Huerga, Akhtar A. Khan, Miguel Sama, A Henig conical regularization approach for circumventing the Slater conundrum in linearly $\ell_{+}^{p}$-constrained least squares problems

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DOI: 10.23952/jano.1.2019.2.03
Volume 1, Issue 2, 31 August 2019, Pages 117-129

Abstract. In this paper, we study a linearly $\ell _{+}^{p}$-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, $p\in \lbrack 1,\infty ),$ we provide an explicit characterization of the Henig dilating cones associated with $\ell _{+}^{p}$ and the associated regularized KKT systems. For the non-separable case $\ell_{+}^{\infty },$ 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.

Lidia Huerga, Akhtar A. Khan, Miguel Sama, A  Henig conical regularization approach for circumventing the Slater conundrum in linearly $\ell_{+}^{p}$-constrained least squares problems, J. Appl. Numer. Optim. 1 (2019), 117-129.