RLT-POS: reformulation-linearization technique-based optimization software for solving polynomial programming problems.

*(English)*Zbl 1353.65052Summary: In this paper, we introduce a reformulation-linearization technique-based open-source optimization software for solving polynomial programming problems (RLT-POS). We present algorithms and mechanisms that form the backbone of RLT-POS, including constraint filtering techniques, reduced RLT representations, and semidefinite cuts. When implemented individually, each model enhancement has been shown in previous papers to significantly improve the performance of the standard RLT procedure. However, the coordination between different model enhancement techniques becomes critical for an improved overall performance since special structures in the original formulation that work in favor of a particular technique might be lost after implementing some other model enhancement. More specifically, we discuss the coordination between (1) constraint elimination via filtering techniques and reduced RLT representations, and (2) semidefinite cuts for sparse problems. We present computational results using instances from the literature as well as randomly generated problems to demonstrate the improvement over a standard RLT implementation and to compare the performances of the software packages BARON, COUENNE, and SparsePOP with RLT-POS.

##### MSC:

65K05 | Numerical mathematical programming methods |

90C26 | Nonconvex programming, global optimization |

65Y15 | Packaged methods for numerical algorithms |

90C57 | Polyhedral combinatorics, branch-and-bound, branch-and-cut |

##### Keywords:

reformulation-linearization technique (RLT); open-source code; constraint filtering strategies; valid inequalities; reduced RLT representations; polynomial programming; numerical example; nonconvex optimization; comparison of software packages; algorithm; filtering
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\textit{E. Dalkiran} and \textit{H. D. Sherali}, Math. Program. Comput. 8, No. 3, 337--375 (2016; Zbl 1353.65052)

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