By using the iterative technique and Nadler’s theorem, we construct a new iterative algorithm for solving a system of nonlinear inclusions in Banach spaces. We prove some new existence results of solutions for the system of nonlinear inclusions and discuss the convergence of the sequences generated by the algorithm. As an application, we show the existence of solution for a system of functional...

We present new algorithms for the dynamic generation of scenario trees for multistage stochastic optimization. The different methods described are based on random vectors, which are drawn from conditional distributions given the past and on sample trajectories. The structure of the tree is not determined beforehand, but dynamically adapted to meet a distance criterion, which insures the quality...

We consider an interstage dependent stochastic process whose components follow an autoregressive model with time varying order. At a given time, we give some recursive formulæ linking future values of the process with past values and noises. We then consider multistage stochastic linear programs with uncertain sets depending affinely on such processes. At each stage, dealing with uncertainty us...

In this paper we consider the notion of rectangularity of a set of probability measures, introduced in Epstein and Schneider [4], from a somewhat different point of view. We define rectangularity as a property of dynamic decomposition of a distributionally robust stochastic optimization problem and show how it relates to the modern theory of coherent risk measures. Consequently we discuss robus...

A novel data-driven approach for optimization under uncertainty based on multistage adaptive robust optimization (ARO) and nonparametric kernel density M-estimation is proposed. Different from conventional robust optimization methods, the proposed framework incorporates distributional information to avoid over-conservatism. Robust kernel density estimation with Hampel loss function is employed ...

In order to operate a process which uses immobilized enzymes at constant conversion and constant capacity, the refreshment of the enzyme must be continuous. In this paper, two reactor types with continuous refreshment of the biocatalyst are discussed: the stirred tank and the multistage fluidized bed. A method is presented for dimensioning a reactor in such a way that the costs for the conversi...

Multistage/multiphase is an inherent characteristic of many batch processes, which should be taken into consideration to ensure better batch process monitoring, analysis, quality prediction and improvement. In this paper, a series of stage-oriented multivariate statistical methods on such topics are reviewed. Then, the modeling problem of transition between stage and stage is discussed. A new p...

We report the mechanism and scope of “preferential enrichment”, which is an unusual symmetry-breaking enantiomeric resolution phenomenon that is initiated by the solvent-assisted solid-to-solid transformation of a metastable polymorphic form into a thermodynamically stable one during crystallization from the supersaturated solution of certain kinds of racemic mixed crystals (i.e., solid solutio...

This paper deals with the existence, uniqueness and iterative approximations of solutions for the functional equations and system of functional equations arising in dynamic programming of multistage decision making processes in Banach spaces and complete metric space, respectively. The results presented in this paper unify and generalize many known results in the literature. Some examples which...