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Zbl 0846.90083
Burke, J.V.; Ferris, M.C.
A Gauss-Newton method for convex composite optimization.
(English)
[J] Math. Program. 71, No.2 (A), 179-194 (1995). ISSN 0025-5610; ISSN 1436-4646/e

Summary: An extension of the Gauss-Newton method for nonlinear equations to convex composite optimization is described and analyzed. Local quadratic convergence is establised for the minimization of $h\circ F$ under two conditions, namely $h$ has a set of weak sharp minima, $C$, and there is a regular point of the inclusion $F(x)\in C$. This result extends a similar convergence result due to Womersley (1985) which employs the assumption of a strongly unique solution of the composite function $h\circ F$. A backtracking line-search is proposed as a globalization strategy. For this algorithm, a global convergence result is established, with a quadratic rate under the regularity assumption.
MSC 2000:
*90C25 Convex programming

Keywords: weak sharp minima; local quadratic convergence; Gauss-Newton method; convex composite optimization

Cited in: Zbl 1049.90132

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