Differential stability of solutions to parametric optimization problems | Zendy

Rao Murali | Zendy; Sokolowski Jan | Zendy

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Differential stability of solutions to parametric optimization problems

Author(s) -

Rao Murali,

Sokolowski Jan

Publication year - 1991

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.1670140405

Subject(s) - mathematics , sobolev space , parametric statistics , stability (learning theory) , projection (relational algebra) , mathematical analysis , optimization problem , metric (unit) , differential equation , mathematical optimization , algorithm , statistics , operations management , machine learning , computer science , economics

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 H 2 (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.

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