Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO. (English) Zbl 1346.90677
Summary: This manuscript reviews recent advances in deterministic global optimization for Mixed-Integer Nonlinear Programming (MINLP), as well as Constrained Derivative-Free Optimization (CDFO). This work provides a comprehensive and detailed literature review in terms of significant theoretical contributions, algorithmic developments, software implementations and applications for both MINLP and CDFO. Both research areas have experienced rapid growth, with a common aim to solve a wide range of real-world problems. We show their individual prerequisites, formulations and applicability, but also point out possible points of interaction in problems which contain hybrid characteristics. Finally, an inclusive and complete test suite is provided for both MINLP and CDFO algorithms, which is useful for future benchmarking.
MSC:
| 90C26 | Nonconvex programming, global optimization |
| 90C11 | Mixed integer programming |
| 90C56 | Derivative-free methods and methods using generalized derivatives |
| 90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |
Software:
DFBOX_IMPR; DFLGEN; DFLBOX; DFN; ROSE; SCIP; GLOPEQ; MINLP; SNOBFIT; SeDuMi; NOMAD; OrthoMADS; APOGEE; MultiMin; GloptiPoly; FEASPUMP; AMPL; ANTIGONE; SDBOX; RealPaver; Biq Mac; MCS; MINLPLib; SDPEN; Boost; AQUARS; GLOPTLAB; MLMSRBF; CGLS; LINDOGlobal; libMC; Boost Interval Arithmetic; DFL; GloMIQO; Bonmin; EGO; LINDO; BARON; PSwarmReferences:
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