Evaluating an element of the Clarke generalized Jacobian of a composite piecewise differentiable function

• DOI: 10.1145/2491491.2491493
• Publication Date: 2013-07-24T13:26:35Z
• Authors: Kamil A. Khan; Paul I. Barton
• Keywords: 0211 other engineering and technologies; 02 engineering and technology

Bundle methods for nonsmooth optimization and semismooth Newton equation solving both require computation of elements the (Clarke) generalized Jacobian, which provides slope information locally Lipschitz continuous functions. Since Jacobian does not obey sharp calculus rules, this can be difficult. In article, are developed evaluating a function that is expressed as finite composition known elemental piecewise differentiable principle, these functions include any whose analytical directional derivatives known. The fully automatable, shown to computationally tractable relative cost evaluation. An implementation in C++ discussed, applied several example problems illustration.