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Constrained minimization for monotonic reconstruction

The authors present several innovations in a method for monotonic reconstructions. It is based on the application of constrained minimization techniques for the imposition of monotonicity on a reconstruction. In addition, they present extensions of several classical TVD limiters to a genuinely multidimensional setting. In this case the linear least squares reconstruction method is expanded upon. They also clarify data dependent weighting techniques used with the minimization process.