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Nonsmooth Optimization

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1989)

Abstract

In the classical Mathematical Analysis, the functions under study are, mostly, differentiable. Nonsmooth Analysis came into being in the 60’s of the XXth century. Its appearance was requested by practical problems of industry, airspace engineering, economics, other sciences where nonsmooth mathematical models were employed to describe more adequately the processes to be investigated. One of the most important problems in Mathematical Analysis is that of finding extremal values of a functional. The same is true in Nonsmooth Analysis. In the present notes, the problem of finding extremal values of a functional defined on some space is discussed. If there are no constraints on the variables, the problem is called the unconstrained optimization problem. If constraints are present, the problem becomes the constrained optimization one.

Keywords

  • Penalty Function
  • Directional Derivative
  • Constrain Optimization Problem
  • Exact Penalty
  • Nonsmooth Analysis

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Demyanov, V.F. (2010). Nonsmooth Optimization. In: Di Pillo, G., Schoen, F. (eds) Nonlinear Optimization. Lecture Notes in Mathematics(), vol 1989. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11339-0_2

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