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KKT conditions for rank-deficient nonlinear least-square problems with rank-deficient nonlinear constraints
Ansvarlig organisasjon
1999 (engelsk)Inngår i: Medietrender och papperskvalitet, ISSN 0022-3239, Vol. 100, nr 1, s. 145-160Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In nonlinear least-square problems with nonlinear constraints, the function $$left. {(1/2)} right|left. {f_2 (x)} right|_2^2$$ , where f 2 is a nonlinear vector function, is to be minimized subject to the nonlinear constraints f 1(x)=0. This problem is ill-posed if the first-order KKT conditions do not define a locally unique solution. We show that the problem is ill-posed if either the Jacobian of f 1 or the Jacobian of J is rank-deficient (i.e., not of full rank) in a neighborhood of a solution satisfying the first-order KKT conditions. Either of these ill-posed cases makes it impossible to use a standard Gauss�Newton method. Therefore, we formulate a constrained least-norm problem that can be used when either of these ill-posed cases occur. By using the constant-rank theorem, we derive the necessary and sufficient conditions for a local minimum of this minimum-norm problem. The results given here are crucial for deriving methods solving the rank-deficient problem.

sted, utgiver, år, opplag, sider
1999. Vol. 100, nr 1, s. 145-160
Emneord [en]
Nonlinear least squares - optimization - regularization - KKT conditions - rank-deficient nonlinear constraints - rank-deficient nonlinear least-square problems
HSV kategori
Identifikatorer
URN: urn:nbn:se:miun:diva-3805DOI: 10.1023/A:1021721132282Lokal ID: 4395OAI: oai:DiVA.org:miun-3805DiVA, id: diva2:28837
Tilgjengelig fra: 2008-09-30 Laget: 2009-09-21bibliografisk kontrollert

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