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Extended cutting plane method for a class of nonsmooth nonconvex MINLP problems. (English) Zbl 1311.90083
Summary: In this article, a generalization of the $$\alpha$$ECP algorithm to cover a class of nondifferentiable Mixed-Integer NonLinear Programming problems is studied. In the generalization constraint functions are required to be $$f^\circ$$-pseudoconvex instead of pseudoconvex functions. This enables the functions to be nonsmooth. The objective function is first assumed to be linear but also $$f^\circ$$-pseudoconvex case is considered. Furthermore, the gradients used in the $$\alpha$$ECP algorithm are replaced by the subgradients of Clarke subdifferential. With some additional assumptions, the resulting algorithm shall be proven to converge to a global minimum.

##### MSC:
 90C11 Mixed integer programming 90C26 Nonconvex programming, global optimization 90C56 Derivative-free methods and methods using generalized derivatives 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
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##### References:
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