An Algorithm for Minimizing a Certain Class of Quasidifferentiable Functions

Demyanov, V.F., Gamidov, S., & Sivelina, T.I. (1983). An Algorithm for Minimizing a Certain Class of Quasidifferentiable Functions. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-83-122

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Abstract

One interesting and important class of nondifferentiable functions is that produced by smooth compositions of max-type functions. Such functions are of practical value and have been studied extensively by several researchers. We treat them as quasidifferentiable functions and analyze them using quasidifferential calculus.

One special subgroup of this class of functions (namely, the sum of a max-type function and a min-type function) has been studied by T.I. Sivelina. The main feature of the algorithm described in the present paper is that at each step it is necessary to consider a bundle of auxiliary directions and points, of which only one can be chosen for the next step. This requirement seems to arise from the intrinsic nature of nondifferentiable functions.

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