Stability and sensivity analysis for conical regularization of linearly constrained least-squares problems in Hilbert spaces

In this paper we follow the conical regularization approach given in Khan and Sama (2013) [14] for a linearly constrained least-square problem in Hilbert spaces. This regularization can be seen as a family of linearly constrained least-problem that is parametrized by a positive parameter ε. We perform a stability and sensitivity analysis by using set-valued analysis and duality tools. As a consequence, we prove that the stability of the optimal value function, the regularity of the unperturbed problem and the norm boundeness of the regularized multipliers are equivalent properties. Moreover under an additional regularity condition, we prove the stability of the regularized solutions and we find a computation formula for the contingent derivative of the optimal value function in terms of any multiplier of the unperturbed problem and the τw-contingent derivative of the trajectory of regularized solutions. Finally, we provide two examples to illustrate our theoretical results.