Conceptual Newton Method for Solving Multivalued Inclusions: Scalar Case

Nurminski, E.A. ORCID: https://orcid.org/0000-0002-7236-6955 (1979). Conceptual Newton Method for Solving Multivalued Inclusions: Scalar Case. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-79-050

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Abstract

Due to different reasons, the actual state of economic, environmental and even mechanical systems is often known only as a set of possible values of the systems indexes. Another source of uncertainty is an unspecified reaction of the system to the changes in control or unpredicted changes in systems inputs. The theory of set-valued mapping provides the mathematical tools for analysis and construction of such systems and is of great importance to system analysis methodology.

This paper is concerned with one of the basic problems of application of set valued mapping -- solving multivalued inclusions. It uses the original definition of a set valued derivative and develops the Newton-like method for solving this problem. The remarkable feature of the proposed method is a quadratical rate of convergency.

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