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-...

Following up on Rebennack and Kallrath (2012), in this paper, for functions depending on two variables, using refinement heuristics, we automatically construct triangulations subject to the condition that the continuous, piecewise linear approximation, under- or overestimation never deviates...