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Global optimization of mixed-integer models with quadratic and signomial functions: a review. (English) Zbl 1292.90239

Summary: Mixed-integer quadratically-constrained quadratic programs (MIQCQP) and mixed-integer signomial optimization problems (MISO) are two important classes of mixed-integer nonconvex programs (nonconvex MINLP). This review discusses the practical applications of MIQCQP and MISO, and covers algorithms designed to globally optimize them. We also describe numerical optimization software designed to solve these classes of problems.

MSC:

90C26 Nonconvex programming, global optimization
90C11 Mixed integer programming
90C20 Quadratic programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
65K05 Numerical mathematical programming methods
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