Taiwanese Journal of Mathematics

Stable Conical Regularization by Constructible Dilating Cones with an Application to $L^{p}$-constrained Optimization Problems

Baasansuren Jadamba, Akhtar A. Khan, and Miguel Sama

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Abstract

We study a convex constrained optimization problem that suffers from the lack of Slater-type constraint qualification. By employing a constructible representation of the constraint cone, we devise a new family of dilating cones and use it to introduce a family of regularized problems. We establish novel stability estimates for the regularized problems in terms of the regularization parameter. To show the feasibility and efficiency of the proposed framework, we present applications to some $L^{p}$-constrained least-squares problems.

Article information

Source
Taiwanese J. Math., Volume 23, Number 4 (2019), 1001-1023.

Dates
Received: 10 January 2018
Revised: 23 July 2018
Accepted: 1 November 2018
First available in Project Euclid: 18 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1563436878

Digital Object Identifier
doi:10.11650/tjm/181103

Mathematical Reviews number (MathSciNet)
MR3982071

Zentralblatt MATH identifier
07088957

Subjects
Primary: 90C20: Quadratic programming 90C31: Sensitivity, stability, parametric optimization 90C46: Optimality conditions, duality [See also 49N15]

Keywords
perturbation theory convex optimization half-space representation conical regularization dilating cones

Citation

Jadamba, Baasansuren; Khan, Akhtar A.; Sama, Miguel. Stable Conical Regularization by Constructible Dilating Cones with an Application to $L^{p}$-constrained Optimization Problems. Taiwanese J. Math. 23 (2019), no. 4, 1001--1023. doi:10.11650/tjm/181103. https://projecteuclid.org/euclid.twjm/1563436878


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