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We investigate multitask learning in the context of multivariate linear regression with high dimensional covariates and heavy‐tailed noise, while under the constraint of limited memory. To tackle the computational complexity arising from the non‐smoothness of the quantile loss, we reformulate it as an equivalent least squares loss, which yields robust solutions even in the presence of heavy‐tailed noise. We incorporate a group lasso penalty into the quantile loss to produce sparse solutions, and an accelerated proximal sub‐gradient descent algorithm to speed up the computation while ensuring explicit forms for penalized solutions at each iteration. The proposed algorithm is general and can be applied to similar optimization problems. Moreover, we introduce a communication‐efficient distributed algorithm that guarantees optimal convergence rates after finite communication rounds in cases where computing resources such as memory are insufficient. We also study the theoretical properties of the resultant estimate and relax the widely used model selection consistency assumption on the initial estimate. We demonstrate the effectiveness of our proposal through extensive numerical studies. [ABSTRACT FROM AUTHOR]

This article focuses on a novel optimization problem to retrofit a conventional fossil‐based refinery into a hybrid biomass‐based refinery. A mixed‐integer linear programming model, which considers a 10‐year‐long retrofit planning along with operational constraints in each year, is formulated. The problem is extended to a multistage stochastic programming model to handle both endogenous and exogenous uncertainties, and solved through a series of two‐stage stochastic programming subproblems. Furthermore, a Lagrangean decomposition algorithm is implemented to solve such a problem. By determining whether to add new units or retrofit existing units to the selected biomass‐based technologies, the results provide flexible design alternatives with consideration of operational constraints for each year. The results show the advantages of the selected biomass‐based technologies and enhance the performance of the final solution under uncertainty. [ABSTRACT FROM AUTHOR]

Bayesian optimization employs probabilistic surrogate models to effectively address expensive and time‐consuming closed‐loop chemical experimental design. However, traditional Bayesian optimization focuses on reducing the number of iterations and follows an inherently sequential process (with one new data point sampled in each iteration), which is an inefficient means of exploiting and characterizing reactions using parallel microreactors. In this article, we present an approach that overcomes this issue by considering two essential factors: experimental cost sensitivity and parallelization. We propose a novel cost‐aware parallelized Bayesian optimization method (CAPBO) in which the goal is changed from reducing the number of iterations to reducing the experimental cost, with quantitative experimental speed‐up achieved through parallelization. The combination of these two items greatly fits the need of reaction optimization, leading to better optimization effects. Benchmarking and case studies demonstrate that the proposed method significantly outperforms traditional Bayesian optimization and considerably improves the optimization efficiency while maintaining the simplicity of the framework. [ABSTRACT FROM AUTHOR]

Sparse quantile regression is a useful tool for variable selection, robust estimation and heteroscedasticity treatment in high-dimensional data analysis. Due to the non-smooth of quantile loss, the computation is heavier than the least square models. In the literature, there are various numerical methods for linear quantile regression, such as ADMM developed in Gu et al. [Technometrics. 2017;60(3):319–331]. However, the computation of multivariate quantile regression has not yet been fully resolved, especially when the dimension is high. Motivated by this, we will focus on the design of fast numerical algorithms for row-sparse multivariate quantile regression model. By virtue of proximal operator and Majorize–Minimization, four smoothed algorithms are designed. For all the obtained algorithms, we analyse their convergence and the parameter selection. We conduct plenty of simulations and four real data sets analysis. Finally, we conclude that the smoothed method is faster than the non-smooth method, especially when the number of predictors is large. [ABSTRACT FROM AUTHOR]