The Rise of Nonsmooth Analysis: Its Main Tools

Authors:
V. F. Demyanov
Affiliations:
St. Petersburg State University, Russia
Venue:
Cybernetics and Systems Analysis
Year:
2002

Citing 3
Cited 0

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Abstract

The main notion in the classical (smooth) mathematical analysis is that of gradient. Nonsmooth analysis deals with nondifferentiable functions, therefore, the problem is to find a proper replacement for the concept of gradient. Different scientific schools use different tools and, as a result, they construct different theories that allow treating different nonsmooth function classes and to solve different nonsmooth problems. Several notions and tools used in nonsmooth analysis and nondifferentiable optimization are discussed.