This paper addresses the discrete network design problem (DNDP) with multiple capacity levels, or multi-capacity DNDP for short, which determines the optimal number of lanes to add to each candidate link in a road network. We formulate the problem as a bi-level programming model, where the upper...

In this paper, we present the derivation of the multiparametric disaggregation technique (MDT) by Teles et al. (J. Glob. Optim., <CitationRef CitationID="CR30">2011</CitationRef>) for solving nonconvex bilinear programs. Both upper and lower bounding formulations corresponding to mixed-integer linear programs are derived using disjunctive...</citationref>

For univariate functions, we compute optimal breakpoint systems subject to the condition that the piecewise linear approximation (or, under- and overestimator) never deviates more than a given δ-tolerance from the original function, over a given finite interval. The linear approximators, under-...