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— When unmanned aerial vehicles (UAVs) are used to survey distant targets, it is important to transmit sensor information back to a base station. As this communication often requires high uninterrupted bandwidth, the surveying UAV often needs a free line-of-sight to the base station, which can be problematic in urban or mountainous areas. Communication(More)
We consider a constrained optimization problem with mixed integer and real variables. It models optimal placement of communications relay nodes in the presence of obstacles. This problem is widely encountered, for instance, in robotics, where it is required to survey some target located in one point and convey the gathered information back to a base station(More)
When unmanned aerial vehicles (UAVs) are used for surveillance, information must often be transmitted to a base station in real time. However, limited communication ranges and the common requirement of free line of sight may make direct transmissions from distant targets impossible. This problem can be solved using relay chains consisting of one or more(More)
Monotonic regression (MR) is an efficient tool used for estimating functions that are monotonic with respect to input variables. We have recently developed a fast high-accuracy approximate algorithm, called GPAV. It allows solving efficiently large-scale multivariate MR problems. We present here an approach which extends the area of its applications to much(More)
We consider the problem of minimizing the distance from a given n-dimensional vector to a set defined by constraints of the form xi ≤ xj. Such constraints induce a partial order of the components xi, which can be illustrated by an acyclic directed graph. This problem is also known as the isotonic regression (IR) problem. IR has important applications in(More)
An important use of unmanned aerial vehicles is surveillance of distant targets, where sensor information must quickly be transmitted back to a base station. In many cases, high uninterrupted bandwidth requires line-of-sight between sender and transmitter to minimize quality degradation. Communication range is typically limited, especially when smaller UAVs(More)
We suggest here a least-change correction to available finite element (FE) solution. This postprocessing procedure is aimed at recovering the monotonicity and some other important properties that may not be exhibited by the FE solution. Although our approach is presented for FEs, it admits natural extension to other numerical schemes, such as finite(More)
Monotonic regression is a non-parametric method that is designed especially for applications in which the expected value of a response variable increases or decreases in one or more explanatory variables. Here, we show how the recently developed generalised pool-adjacent-violators (GPAV) algorithm can greatly facilitate the assessment of trends in time(More)