×
Eronen, Ville-Pekka; Mäkelä, Marko M.; Westerlund, Tapio

Extended cutting plane method for a class of nonsmooth nonconvex MINLP problems. (English) Zbl 1311.90083

Optimization 64, No. 3, 641-661 (2015).
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.

Cited in 6 Documents

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

Keywords:

nonsmooth MINLP; mixed-integer programming; nonsmooth optimization; extended cutting plane algorithm; \(\alpha\)ECP; subgradient; pseudoconvex function; generalized convexity
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.1016/0098-1354(95)87027-X · doi:10.1016/0098-1354(95)87027-X
[2] DOI: 10.1016/0098-1354(92)80028-8 · doi:10.1016/0098-1354(92)80028-8
[3] DOI: 10.1007/BF02592064 · Zbl 0619.90052 · doi:10.1007/BF02592064
[4] DOI: 10.1007/BF01581153 · Zbl 0833.90088 · doi:10.1007/BF01581153
[5] DOI: 10.1016/0255-2701(89)80035-2 · doi:10.1016/0255-2701(89)80035-2
[6] Emet S, Comput. Chem. Eng. 28 pp 673– (2004) · doi:10.1016/j.compchemeng.2004.02.010
[7] DOI: 10.1007/978-3-642-82118-9 · doi:10.1007/978-3-642-82118-9
[8] DOI: 10.1142/1493 · doi:10.1142/1493
[9] Clarke FH, Optimization and nonsmooth analysis (1983)
[10] DOI: 10.1007/BF02192119 · Zbl 0824.90124 · doi:10.1007/BF02192119
[11] Jain V, AIChE J. 44 pp 1623– (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.