Joint Routing of Conventional and Range-Extended Electric Vehicles in a Large Metropolitan Network

Range-extended electric vehicles combine the higher efficiency and environmental benefits of battery-powered electric motors with the longer mileage and autonomy of conventional internal combustion engines. This combination is particularly advantageous for time-constrained delivery routing in dense urban areas, where battery recharging along routes can be too time-consuming to economically justify the use of all-electric vehicles. … Read more

Derivative-free optimization methods

In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in … Read more

A Method for Convex Black-Box Integer Global Optimization

We study the problem of minimizing a convex function on the integer lattice when the function cannot be evaluated at noninteger points. We propose a new underestimator that does not require access to (sub)gradients of the objective but, rather, uses secant linear functions that interpolate the objective function at previously evaluated points. These linear mappings … Read more

Manifold Sampling for Optimization of Nonconvex Functions that are Piecewise Linear Compositions of Smooth Components

We develop a manifold sampling algorithm for the minimization of a nonsmooth composite function $f \defined \psi + h \circ F$ when $\psi$ is smooth with known derivatives, $h$ is a known, nonsmooth, piecewise linear function, and $F$ is smooth but expensive to evaluate. The trust-region algorithm classifies points in the domain of $h$ as … Read more

Manifold Sampling for L1 Nonconvex Optimization

We present a new algorithm, called manifold sampling, for the unconstrained minimization of a nonsmooth composite function $h\circ F$ when $h$ has known structure. In particular, by classifying points in the domain of the nonsmooth function $h$ into manifolds, we adapt search directions within a trust-region framework based on knowledge of manifolds intersecting the current … Read more

Derivative-free Optimization of Expensive Functions with Computational Error Using Weighted Regression

We propose a derivative-free algorithm for optimizing computationally expensive functions with computational error. The algorithm is based on the trust region regression method by Conn, Scheinberg, and Vicente [4], but uses weighted regression to obtain more accurate model functions at each trust region iteration. A heuristic weighting scheme is proposed which simultaneously handles i) differing … Read more