This paper presents a mixed-integer quadratically constrained programming (MIQCP) formulation for B-spline constraints. The formulation can be used to obtain an exact MIQCP reformulation of any spline-constrained optimization problem, provided that the polynomial spline functions are continuous. This reformulation allows practitioners to use a general-purpose MIQCP solver, instead of a special-purpose spline solver, when solving B-spline constrained problems. B-splines are a powerful and widely used modeling tool, previously restricted from optimization due to lack of solver support. This contribution may encourage practitioners to use B-splines to model constraint functions. However, as the numerical study suggests, there is still a large gap between the solve times of the general-purpose solvers using the proposed formulation, and the special-purpose spline solver CENSO , the latter being significantly lower.
Bjarne Grimstad (email@example.com) Department of Engineering Cybernetics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway February 9, 2017