We consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. https://doi.org/10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise...

We revisit the problem of computing optimal spline approximations for univariate least-squares splines from a combinatorial optimization perspective. In contrast to most approaches from the literature we aim at globally optimal coefficients as well as a globally optimal placement of a fixed...

In this paper, we develop an algorithm for minimizing the L <Subscript> q </Subscript> norm of a vector whose components are linear fractional functions, where q is an arbitrary positive integer. The problem is a kind of sum-of-ratios optimization problem, and often occurs in computer vision. In that case, it is...</subscript>

Abstract Spatial branch-and-bound algorithms for global minimization of non-convex problems require both lower and upper bounding procedures that finally converge to a globally optimal value in order to ensure termination of these methods. Whereas convergence of lower bounds is commonly...