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Zbl 0555.90086
Gafni, Eli M.; Bertsekas, Dimitri P.
Two-metric projection methods for constrained optimization. (English)
[J] SIAM J. Control Optimization 22, 936-964 (1984). ISSN 0363-0129; ISSN 1095-7138/e

The authors propose an algorithm for solving the problem min f(x), s.t. $x\in X$, with X a closed convex subset of the Hilbert space H and f:H$\to {\bbfR}\sp a $smooth function of the form $x\sb{k+1}=P(X\sb k$- $\alpha$ ${}\sb kg\sb k)$, where $g\sb k=\nabla f(x\sb k)$ and P denotes the projection on X. The norms $\Vert \cdot \Vert$ and $\Vert \cdot \Vert\sb k$ corresponding to the projection on X and the differentiation operators are generally different, depending on the structure of X and the Hessian of f at $x\sb k$, respectively. Under some additional assumptions the algorithm attains a superlinear rate of convergence.
[C.Zălinescu]

MSC 2000:: *90C30 Nonlinear programming
49M37 Methods of nonlinear programming type

Keywords: two-metric projection methods; constrained optimization; gradient projection; convergence analysis; multicommodity flow problems; large- scale optimization; Hilbert space; superlinear rate of convergence

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