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Two-metric projection methods for constrained optimization. (English) Zbl 0555.90086
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\(\to {\mathbb{R}}^ a \)smooth function of the form \(x_{k+1}=P(X_ k\)- \(\alpha\) \({}_ kg_ k)\), where \(g_ k=\nabla f(x_ k)\) and P denotes the projection on X. The norms \(\| \cdot \|\) and \(\| \cdot \|_ k\) 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 \(x_ k\), respectively. Under some additional assumptions the algorithm attains a superlinear rate of convergence.
Reviewer: C.Zălinescu

90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
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