Solvability conditions for variational-like inequalities

Authors:
N. B. Shamray
Affiliations:
Institute of Automatics and Managerial Processes, Far East Branch of the Russian Academy of Sciences, Vladivostok, Russia
Venue:
Cybernetics and Systems Analysis
Year:
2008

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Abstract

Solvability conditions are proposed for variational-like inequalities defined on bounded and unbounded feasible sets under the assumption of generalized (quasi-and 0-diagonal) convexity of the mappings used in the problem being solved. Existence and uniqueness conditions are proposed for its solution. Mappings of variational-like inequalities are assumed to be generally convex, strongly monotone, and Lipshitzian.