Granularity in Nonlinear Mixed-Integer Optimization

Christoph Neumann (), Oliver Stein () and Nathan Sudermann-Merx ()
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Christoph Neumann: Karlsruhe Institute of Technology (KIT)
Oliver Stein: Karlsruhe Institute of Technology (KIT)
Nathan Sudermann-Merx: BASF SE

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 2, No 7, 433-465

Abstract: Abstract 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 Neumann et al. (Comput Optim Appl 72:309–337, 2019). 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.

Keywords: Rounding; Granularity; Pseudo-granularity; Inner parallel set; Consistency; 90C11; 90C10; 90C31; 90C30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-019-01591-y

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