Abstract
We consider quasidifferentiable functions in the sense of Demyanov and Rubinov, i. e. functions, which are directionally differentiable and whose directional derivative can be expressed as a difference of two sublinear functions, so that its “subdifferential”, called the quasidifferential, consists of a pair of sets. For these functions a generalized gradient algorithm is proposed. Its behaviour is studied in detail for the special class of continuously subdifferentiable functions. Numerical test results are given. Finally, the general quasidifferentiable case is simulated by means of “perturbed” subdifferentials, where we make use of the non-uniqueness in the quasidifferential representation.
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Luderer, B., Weigelt, J. A Solution Method for a Special Class of Nondifferentiable Unconstrained Optimization Problems. Computational Optimization and Applications 24, 83–93 (2003). https://doi.org/10.1023/A:1021854116784
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DOI: https://doi.org/10.1023/A:1021854116784