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Generalized Gradient Methods of Nondifferentiable Optimization Employing Space Dilatation Operations

In: Mathematical Programming The State of the Art

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  • N. Z. Shor

    (Academy of Sciences of the Ukrainian SSR, V. M. Glushkov, Institute of Cybernetics)

Abstract

A broad spectrum of complex problems of mathematical programming can be rather easily reduced to problems of minimization of nondifferentiable functions without constraints or with simple constraints. Thus, when decomposition schemes are used to solve structured optimization problems of large dimension or with a large number of constraints, the coordination problems with respect to linking variables (or dual estimates of linking constraints) as a rule prove to be problems of nondifferentiable optimization. The use of exact nonsmooth penalty functions in problems of nonlinear programming, maximum functions to estimate discrepancies in constraints, piecewise smooth approximation of technical-economic characteristics in practical problems of optimal planning and design, minimax compromise functions in problems of multi-criterion optimization, all of these generate problems of nondifferentiable optimization. Therefore, the efficiency of procedures for the solution of various complex problems of mathematical programming greatly depends on the efficiency of the algorithms employed to minimize nondifferentiable functions.

Suggested Citation

  • N. Z. Shor, 1983. "Generalized Gradient Methods of Nondifferentiable Optimization Employing Space Dilatation Operations," Springer Books, in: Achim Bachem & Bernhard Korte & Martin Grötschel (ed.), Mathematical Programming The State of the Art, pages 501-529, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-68874-4_19
    DOI: 10.1007/978-3-642-68874-4_19
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