Abstract
This paper studies how the solution of the problem of minimizingQ(x) = 1/2x T Kx − k T x subject toGx ≦ g andDx = d behaves whenK, k, G, g, D andd are perturbed, say by terms of size∈, assuming thatK is positive definite. It is shown that in general the solution moves by roughly∈ ifG, g, D andd are not perturbed; whenG, g, D andd are in fact perturbed, much stronger hypotheses allow one to show that the solution moves by roughly∈. Many of these results can be extended to more general, nonquadratic, functionals.
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This research was supported in part by contract number N00014-67-A-0126-0015, NR 044-425 from the Office of Naval Research.
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Daniel, J.W. Stability of the solution of definite quadratic programs. Mathematical Programming 5, 41–53 (1973). https://doi.org/10.1007/BF01580110
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DOI: https://doi.org/10.1007/BF01580110