The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [IMA Journal of Numerical Analysis, 8 (1988)] has driven us to consider a globalization strategy based on SD, which is applicable to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. … Read more
The Traveling Salesperson Problem with Drone (TSP–D) is a routing model in which a given set of customer locations must be visited in the least amount of time, either by a truck route starting and ending at a depot or by a drone dispatched from the truck en route. We study the TSP–D model and … Read more
We present a stochastic optimization model for allocating and sharing a critical resource in the case of a pandemic. The demand for different entities peaks at different times, and an initial inventory for a central agency is to be allocated. The entities (states) may share the critical resource with a different state under a risk-averse … Read more
In the paper of Rocha et al., J Optim Theory Appl (2016) 171:964979, the authors introduced a proximal point algorithm with quasi-distances to solve unconstrained convex multi-objective minimization problems. They proved that all accumulation points are ecient solutions of the problem. In this pa- per we analyze an inexact proximal point algorithm to solve convex … Read more
We consider a class of stochastic programs whose uncertain data has an exponential number of possible outcomes, where scenarios are affinely parametrized by the vertices of a tractable binary polytope. Under these conditions, we propose a novel formulation that introduces a modest number of additional variables and a class of inequalities that can be efficiently … Read more
Healthcare facilities are struggling in fighting the spread of COVID-19. While machines needed for patients such as ventilators can be built or bought, healthcare personnel is a very scarce resource that cannot be increased by hospitals in a short period. Furthermore, healthcare personnel is getting sick while taking care of infected people, increasing this shortage … Read more
We study a mobile facility (MF) routing and scheduling problem in which probability distributions of the time-dependent demand for MF services is unknown. To address distributional ambiguity, we propose and analyze two distributionally robust MF routing and scheduling (DMFRS) models that seek to minimize the fixed cost of establishing the MF fleet and maximum expected … Read more
For nonconvex optimization problems, possibly having mixed-integer variables, a convergent primal-dual solution algorithm is proposed. The approach applies a proximal bundle method to certain augmented Lagrangian dual that arises in the context of the so-called generalized augmented Lagrangians. We recast these Lagrangians into the framework of a classical Lagrangian, by means of a special reformulation … Read more
In this letter, we present an alternative mixed-integer non-liner programming formulation of the reactive optimal power flow (ROPF) problem. We utilize a mixed-integer second-order cone programming (MISOCP) based approach to find global optimal solutions of the proposed ROPF problem formulation. We strengthen the MISOCP relaxation via the addition of convex envelopes and cutting planes. Computational … Read more
In many routing applications, it is necessary to place limits on the duration of the individual routes. When demands are stochastic and restocking during route execution is allowed, the durations of the resulting routes are also stochastic. In this paper, we consider the vehicle routing problem with stochastic demands and (probabilistic) duration constraints (VRPSD-DC). We … Read more