×

zbMATH — the first resource for mathematics

Review of nonlinear mixed-integer and disjunctive programming techniques. (English) Zbl 1035.90050
Summary: This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, branch and bound, outer-approximation, generalized Benders and extended cutting plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.

MSC:
90C11 Mixed integer programming
90C30 Nonlinear programming
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
Software:
BARON; LogMIP
PDF BibTeX Cite
Full Text: DOI