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This paper presents a solution method for parametric linear complementarity problems (PLCP) that relies on an enumeration technique to discover all feasible bases. The enumeration procedure is based on evaluating all possible combinations of active constraints and testing for feasibility. Although the enumeration approach is known to grow exponentially in the number of constraints, the formulation of the PLCP allows incorporation of cheap rank tests to quickly prune the infeasible directions in the exploration. The motivation for the development of the enumeration based PLCP solver is that it represents a direct method to solve parametric linear and quadratic optimization problems as well as their mixed-integer counterparts. These types of problems often arise in the field of model predictive control for linear and hybrid systems. The enumeration based PLCP solver offers another alternative to compute explicit solutions in the field of hybrid model predictive control that can be extremely effective in some important cases.

This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.

In this paper we study the solution to optimal control problems for constrained discrete-time linear hybrid systems based on quadratic or linear performance criteria. The aim of the paper it twofold. First we give basic theoretical results on the structure of the optimal state feedback solution and of the value function. Second we describe how the state feedback optimal control law can be efficiently constructed by combining multiparametric programming and dynamic programming.