Differential stability of solutions to parametric optimization problems
Murali Rao, Jan Sokołowski · Mathematical Methods in the Applied Sciences · 1991
Abstract A method for the differential stability of solutions to a class of solutions to a class of parametric optimization problem is prposed. Any solution of the parametric optimization problem is given as a fixed point of the metric projection onto the set of admissible coefficients. A new result on the differential stability of the metric projection in Sobolev space H2(Ω)onto a set of admissible parameters is obtained. The stability results with respect to perturbations of observations for the solutions to a coefficient estimation problem for a second‐order elliptic equation are derived.