Of recent coinage, the term "nondifferentiable optimization" (NDO)
covers a spectrum of problems related to finding extremal values of
nondifferentiable functions. Problems of minimizing nonsmooth
functions arise in engineering applications as well as in
mathematics proper. The Chebyshev approximation problem is an ample
illustration of this. Without loss of generality, we shall consider
only minimization problems. Among nonsmooth minimization problems,
minimax problems and convex problems have been studied extensively
([31], [36], [57], [110], [120]). Interest in NDO has been
constantly growing in recent years (monographs: [30], [81], [127]
and articles and papers: [14], [20], [87]-[89], [98], [130], [135],
[140]-[142], [152], [153], [160], all dealing with various aspects
of non smooth optimization). For solving an arbitrary minimization
problem, it is neces sary to: 1. Study properties of the objective
function, in particular, its differentiability and directional
differentiability. 2. Establish necessary (and, if possible,
sufficient) condi tions for a global or local minimum. 3. Find the
direction of descent (steepest or, simply, feasible--in appropriate
sense). 4. Construct methods of successive approximation. In this
book, the minimization problems for nonsmooth func tions of a
finite number of variables are considered. Of fun damental
importance are necessary conditions for an extremum (for example,
[24], [45], [57], [73], [74], [103], [159], [163], [167], [168].
General
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