A Gauss—Newton method for convex composite optimization
نویسندگان
چکیده
منابع مشابه
A Gauss - Newton method for convex composite optimization 1
An extension of the Gauss-Newton method for nonlinear equations to convex composite optimization is described and analyzed. Local quadratic convergence is established for the minimization of h o 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) E C. This result extends a similar convergence result due to Womersley (this journa...
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An extension of the Gauss{Newton method for nonlinear equations to convex composite optimization is described and analyzed. Local quadratic convergence is established for the minimization of h 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) 2 C. This result extends a similar convergence result due to Womersley which employs ...
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xi=x̄i when ‖∇xif(x̄)‖2 ≤ λBi, it follows that x̄i = x̄i if and only if ‖∇xif(x̄)‖2 ≤ λBi. Hence, hi(x̄ ∗ i ) = 0. Case 2: Suppose that i ∈ Ic := N \ I, i.e., ‖∇xif(x̄)‖2 > λBi. In this case, x̄i 6= x̄i. From the first-order optimality condition, we have ∇xif(x̄) + Li(x̄i − x̄i) + λBi x̄ ∗ i −x̄i ‖x̄i −x̄i‖2 = 0. Let si := x̄∗i −x̄i ‖x̄i −x̄i‖2 and ti := ‖x̄i − x̄i‖2, then si = −∇xif(x̄) Liti+λBi . Since ‖si‖2 = 1, i...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 1995
ISSN: 0025-5610,1436-4646
DOI: 10.1007/bf01585997