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...

Machine learning (ML) is a novel method that has applications in asset pricing and that fits well within the problem of measurement in economics. Unlike econometrics, ML models are not designed for parameter estimation and inference, but similar to econometrics, they address, and may be better...

In this paper, we offer a novel class of utility functions applied to optimal portfolio selection. This class incorporates as special cases important measures such as the mean-variance, Sharpe ratio, mean-standard deviation and others. We provide an explicit solution to the problem of optimal...

To explore the problems associated with applying dynamic programming (DP) in the energy management strategies of plug-in hybrid electric vehicles (PHEVs), a plug-in hybrid bus powertrain is introduced and its dynamic control model is constructed. The numerical issues, including the...

We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard...

We consider the computational complexity of optimizing various classes of continuous functions over a simplex, hypercube or sphere.These relatively simple optimization problems have many applications.We review known approximation results as well as negative (inapproximability) results from the...

The classic Kriging variance formula is widely used in geostatistics and in the design and analysis of computer experiments.This paper proves that this formula is wrong.Furthermore, it shows that the formula underestimates the Kriging variance in expectation.The paper develops parametric...

In this paper simulated annealing algorithms for continuous global optimization are considered.Under the simplifying assumption of known optimal value, the convergence of the algorithms and an upper bound for the expected first hitting time, i.e. the expected number of iterations before reaching...