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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

##### MSC:
 90C30 Nonlinear programming 49M37 Numerical methods based on nonlinear programming
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