Geodesic
Computing minimum norm solution of a specific constrained convex nonlinear problem
Kybernetika, Tome 48 (2012) no. 1, pp. 123-129 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The characterization of the solution set of a convex constrained problem is a well-known attempt. In this paper, we focus on the minimum norm solution of a specific constrained convex nonlinear problem and reformulate this problem as an unconstrained minimization problem by using the alternative theorem.The objective function of this problem is piecewise quadratic, convex, and once differentiable. To minimize this function, we will provide a new Newton-type method with global convergence properties.
The characterization of the solution set of a convex constrained problem is a well-known attempt. In this paper, we focus on the minimum norm solution of a specific constrained convex nonlinear problem and reformulate this problem as an unconstrained minimization problem by using the alternative theorem.The objective function of this problem is piecewise quadratic, convex, and once differentiable. To minimize this function, we will provide a new Newton-type method with global convergence properties.
Classification : 90C05, 90C51
Keywords: solution set of convex problems; alternative theorems; minimum norm solution; residual vector 
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Ketabchi, Saeed; Moosaei, Hossein. Computing minimum norm solution of a specific constrained convex nonlinear problem. Kybernetika, Tome 48 (2012) no. 1, pp. 123-129. http://geodesic.mathdoc.fr/item/KYB_2012_48_1_a6/

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