The Nonlocal Newton Method for Convex Optimization Problems and Monotone Variational Inequalities

Authors:
V. M. Panin;V. V. Skopetskii
Affiliations:
Scientific and Training Center "Institute of Applied Systems Analysis" of the National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, Kiev, Ukraine nmo@mm ...;Institute of Cybernetics, National Academy of Sciences of Ukraine, Kiev, Ukraine fiotkpi@public.icyb.kiev.ua
Venue:
Cybernetics and Systems Analysis
Year:
2002

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Abstract

The nonlocal Newton method is developed for nonlinear problems of conditional convex optimization and monotone variational inequalities in a finite-dimensional space. The Newton direction vector is calculated from a solution of a linear-approximating variational inequality. A new penalty function is proposed to define a step length.