zbMATH — the first resource for mathematics

Computing minimum norm solution of a specific constrained convex nonlinear problem. (English) Zbl 1244.90181
Summary: 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.
90C25 Convex programming
90C51 Interior-point methods
Full Text: EuDML Link
[1] L. Armijo: Minimazation of functions having Lipschitz-continuous first partial derivatives. Pacific J. Math. 16 (1966), 1-3. · Zbl 0202.46105
[2] Yu. G. Evtushenko, A. I. Golikov: New perspective on the theorems of alternative. High Performance Algorithms and Software for Nonlinear Optimization, Kluwer Academic Publishers B.V., 2003, pp. 227-241. · Zbl 1044.90088
[3] A. I. Golikov, Yu. G. Evtushenko: Theorems of the alternative and their applications in numerical methods. Comput. Math. and Math. Phys. 43 (2003), 338-358.
[4] C. Kanzow, H. Qi, L. Qi: On the minimum norm solution of linear programs. J. Optim. Theory Appl. 116 (2003), 333-345. · Zbl 1043.90046
[5] S. Ketabchi, E. Ansari-Piri: On the solution set of convex problems and its numerical application. J. Comput. Appl. Math. 206 (2007), 288-292. · Zbl 1131.90042
[6] O. L. Magasarian: A simple characterization of solution sets of convex programs. Oper. Res. Lett. 7 (1988), 21-26. · Zbl 0653.90055
[7] O. L. Magasarian: A Newton method for linear programming. J. Optim. Theory Appl. 121 (2004), 1-18. · Zbl 1140.90467
[8] O. L. Magasarian: A finite Newton method for classification. Optim. Meth. Software 17 (2002), 913-930. · Zbl 1065.90078
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.