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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.

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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[1] DOI: 10.1016/0098-1354(95)87027-X
[2] DOI: 10.1016/0098-1354(92)80028-8
[3] DOI: 10.1007/BF02592064 · Zbl 0619.90052
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[10] DOI: 10.1007/BF02192119 · Zbl 0824.90124
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