Recent advances in multiparametric nonlinear programming

Multi Set-Point Explicit Model Predictive Control for Nonlinear Process Systems

In this article, we introduce a novel framework for the design of multi set-point nonlinear explicit controllers for process systems engineering problems where the set-points are treated as uncertain parameters simultaneously with the initial state of the dynamical system at each sampling instance. To this end, an algorithm for a special class of multi-parametric nonlinear programming problems with uncertain parameters on the right-hand side of the constraints and the cost coefficients of the objective function is presented. The algorithm is based on computed algebra methods for symbolic manipulation that enable an analytical solution of the optimality conditions of the underlying multi-parametric nonlinear program. A notable property of the presented algorithm is the computation of exact, in general nonconvex, critical regions that results in potentially great computational savings through a reduction in the number of convex approximate critical regions.

Quantile planes without crossing via nonlinear programming

BACKGROUND AND OBJECTIVE

In this note we propose a nonlinear programming approach for simultaneous fitting of quantile regression models for two or more quantiles. The approach is straightforward, flexible and practical. We apply this approach to a dataset of lactic acid values from a screening dataset in childhood malaria.

METHODS

We carry out the fitting of simultaneous quantile regression models using a specific definition of a quantile as an expectation via nonlinear programming methods given certain monotonicity constraints.

RESULTS

We illustrate through simulations and examples that are new approach to simultaneous quantile regression is practical and feasible. The approach is supplemented by providing a bootstrap framework for confidence interval estimation.

CONCLUSIONS

Our nonlinear programming approach towards solving the simultaneous quantile regression fitting is shown to be a practical approach that should appeal to statistical practitioners.