Rao, Murali; Sokołowski, Jan Differential stability of solutions to parametric optimization problems. (English) Zbl 0749.90077 Math. Methods Appl. Sci. 14, No. 4, 281-294 (1991). Summary: A method for the differential stability of solutions to a class of parametric optimization problems is proposed. 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 \(H^ 2(\Omega)\) 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. Cited in 3 Documents MSC: 90C31 Sensitivity, stability, parametric optimization Keywords:differential stability of solutions; parametric optimization; second- order elliptic equation × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Sobolev Spaces, Academic, New York, 1975. · Zbl 0314.46030 [2] Bamberger, Appl. Math. Optim. 5 pp 1– (1979) [3] ’On th uniqueness of local minima for general abstract non-linear least square problem’, Rapport de Recherche No 645, INRIA, Rocquencourt, France. [4] and , ’Stability of perturbed optimization problems with applications to parameter estimation’, Preprint. [5] Classical Potential Theory and its Probabilistic Counter Part, Springer, New York. 1985. [6] Haraux, J. Math. Soc. Japan 29 pp 615– (1977) [7] Hedberg, Acta Math. 147 pp 237– (1981) [8] Hoffmann, SIAM J. Math. Anal. 5 pp 1198– (1986) [9] Mignot, J. funct. Anal. 22 pp 25– (1976) [10] Rao, Polyhedricity of convex sets in Sobolev space H20 ({\(\omega\)}) [11] and , ’Shape sensitivity analysis of state constrained optimal control problems for distributed parameter systems’, Lecture Notes in Control and Information Sciences, Vol. 114, Springer, Berlin, 1989, pp. 236-245. [12] Sokolowski, Appl. Math. Optim. 13 pp 97– (1985) [13] Sokolowski, SIAM J. Control and Optimization 25 pp 1542– (1987) [14] Sokolowski, Control and Cybernetics. 19 pp 271– (1990) [15] ’Projections on convex sets in Hilbert space and spectral theory’, Contributions to Nonlinear Functional Analysis, Publ. No 27, Mathematical Research Center, University of Wisconsin, Madison, Academic Press, New York, 1971, 237-424. · doi:10.1016/B978-0-12-775850-3.50013-3 [16] Weakly Differentiable Functions, Springer, New York, 1989. · Zbl 0692.46022 · doi:10.1007/978-1-4612-1015-3 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.