Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Holder constants

In this paper, the global optimization problem $\min_{y\in S} F(y)$ with $S$ being a hyperinterval in $\Re^N$ and $F(y)$ satisfying the Lipschitz condition with an unknown Lipschitz constant is considered. It is supposed that the function $F(y)$ can be multiextremal, non-differentiable, and given as a `black-box'. To attack the problem, a new global optimization algorithm based on the following two ideas is proposed and studied both theoretically and numerically. First, the new algorithm uses numerical approximations to space-filling curves to reduce the original Lipschitz multi-dimensional problem to a univariate one satisfying the H\"{o}lder condition. Second, the algorithm at each iteration applies a new geometric technique working with a number of possible H\"{o}lder constants chosen from a set of values varying from zero to infinity showing so that ideas introduced in a popular DIRECT method can be used in the H\"{o}lder global optimization. Convergence conditions of the resulting deterministic global optimization method are established. Numerical experiments carried out on several hundreds of test functions show quite a promising performance of the new algorithm in comparison with its direct competitors.Comment: 26 pages, 10 figures, 4 table

Comparison of different objective functions for parameterization of simple respiration models

The eddy covariance measurements of carbon dioxide fluxes collected around the world offer a rich source for detailed data analysis. Simple, aggregated models are attractive tools for gap filling, budget calculation, and upscaling in space and time. Key in the application of these models is their parameterization and a robust estimate of the uncertainty and reliability of their predictions. In this study we compared the use of ordinary least squares (OLS) and weighted absolute deviations (WAD, which is the objective function yielding maximum likelihood parameter estimates with a double exponential error distribution) as objective functions within the annual parameterization of two respiration models: the Q10 model and the Lloyd and Taylor model. We introduce a new parameterization method based on two nonparametric tests in which model deviation (Wilcoxon test) and residual trend analyses (Spearman test) are combined. A data set of 9 years of flux measurements was used for this study. The analysis showed that the choice of the objective function is crucial, resulting in differences in the estimated annual respiration budget of up to 40%. The objective function should be tested thoroughly to determine whether it is appropriate for the application for which the model will be used. If simple models are used to estimate a respiration budget, a trend test is essential to achieve unbiased estimates over the year. The analyses also showed that the parameters of the Lloyd and Taylor model are highly correlated and difficult to determine precisely, thereby limiting the physiological interpretability of the parameter

Learning to Race through Coordinate Descent Bayesian Optimisation

In the automation of many kinds of processes, the observable outcome can often be described as the combined effect of an entire sequence of actions, or controls, applied throughout its execution. In these cases, strategies to optimise control policies for individual stages of the process might not be applicable, and instead the whole policy might have to be optimised at once. On the other hand, the cost to evaluate the policy's performance might also be high, being desirable that a solution can be found with as few interactions as possible with the real system. We consider the problem of optimising control policies to allow a robot to complete a given race track within a minimum amount of time. We assume that the robot has no prior information about the track or its own dynamical model, just an initial valid driving example. Localisation is only applied to monitor the robot and to provide an indication of its position along the track's centre axis. We propose a method for finding a policy that minimises the time per lap while keeping the vehicle on the track using a Bayesian optimisation (BO) approach over a reproducing kernel Hilbert space. We apply an algorithm to search more efficiently over high-dimensional policy-parameter spaces with BO, by iterating over each dimension individually, in a sequential coordinate descent-like scheme. Experiments demonstrate the performance of the algorithm against other methods in a simulated car racing environment.Comment: Accepted as conference paper for the 2018 IEEE International Conference on Robotics and Automation (ICRA

Decentralized spectral resource allocation for OFDMA downlink of coexisting macro/femto networks using filled function method

For an orthogonal frequency division multiple access (OFDMA) downlink of a spectrally coexisting macro and femto network, a resource allocation scheme would aim to maximize the area spectral efficiency (ASE) subject to constraints on the radio resources per transmission interval accessible by each femtocell. An optimal resource allocation scheme for completely decentralized deployments leads however to a nonconvex optimization problem. In this paper, a filled function method is employed to find the global maximum of the optimization problem. Simulation results show that our proposed method is efficient and effective