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Granularity in nonlinear mixed-integer optimization. (English) Zbl 1433.90089
Summary: We study a new technique to check the existence of feasible points for mixed-integer nonlinear optimization problems that satisfy a structural requirement called granularity. For granular optimization problems, we show how rounding the optimal points of certain purely continuous optimization problems can lead to feasible points of the original mixed-integer nonlinear problem. To this end, we generalize results for the mixed-integer linear case from [the authors, Comput. Optim. Appl. 72, No. 2, 309–337 (2019; Zbl 1414.90239)]. We study some additional issues caused by nonlinearity and show how to overcome them by extending the standard granularity concept to an advanced version, which we call pseudo-granularity. In a computational study on instances from a standard test library, we demonstrate that pseudo-granularity can be expected in many nonlinear applications from practice, and that its explicit use can be beneficial.

90C11 Mixed integer programming
90C30 Nonlinear programming
90C10 Integer programming
90C31 Sensitivity, stability, parametric optimization
Full Text: DOI
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