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Generalized Equations

In: Mathematical Programming The State of the Art

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  • Stephen M. Robinson

    (University of Wisconsin-Madison, Dept. of Industrial Engineering)

Abstract

The term “generalized equation” has recently been used to describe certain kinds of inclusions that involve multivalued functions, particularly normal-cone operators. Such problems include static generalized equations, which extend ordinary nonlinear equations, as well as generalized differential equations, which extend ordinary differential equations to the situation in which the defining relation contains multivalued functions (again, particularly normal-cone operators). This survey gives an overview of what is known about these problems as of late 1982. Because of space limitations, it has not been practical to present an encyclopedic description of all recent work. Rather, this paper tries to exhibit samples of recent results in several different areas, and to lead the reader to works in the literature that explain those results in more detail and that contain references to other work not mentioned here. The choice of samples to be presented was based on the author’s particular knowledge and interests.

Suggested Citation

  • Stephen M. Robinson, 1983. "Generalized Equations," Springer Books, in: Achim Bachem & Bernhard Korte & Martin Grötschel (ed.), Mathematical Programming The State of the Art, pages 346-367, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-68874-4_14
    DOI: 10.1007/978-3-642-68874-4_14
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