A General Iterative Procedure to Solve Generalized Equations with Differentiable Multifunction

Michaël Gaydu () and Gilson N. Silva ()
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Michaël Gaydu: Université Antilles
Gilson N. Silva: Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 1, No 12, 207-222

Abstract: Abstract Taking advantage of recent developments in the theory of generalized differentiation of multifunctions, we present in a unified manner a general iterative procedure for solving generalized equations. This procedure is based on a certain type of approximation of functions called point-based approximation together with a linearization of the multifunctions. Our theorem encompasses the Newton method and extends in the same time, many methods of resolution of generalized equations that have been developed during the last two decades.

Keywords: Generalized equation; Generalized point-based approximations; Differentiable multifunction; Newton method; Metric regularity; 49J53; 49J40; 90C48 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-020-01635-8

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