We study a fine hierarchy of Borel-piecewise continuous functions, especially, between closed-piecewise continuity and Gδ-piecewise continuity. Our aim is to understand how a priority argument in computability theory is connected to the notion of Gδ-piecewise continuity, and then we utilize this connection to obtain separation results on subclasses of Gδ-piecewise continuous reductions for unif...

Piecewise quasilinearization methods for singular boundary-value problems in second-order ordinary differential equations are presented. These methods result in linear constant-coefficients ordinary differential equations which can be integrated analytically, thus yielding piecewise analytical solutions. The accuracy of the globally smooth piecewise quasilinear method is assessed by comparisons...

Abs t r ac t Piecewise linear models systems arise os mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous o r discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phose por...

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method extends in a natural way a linearization scheme that was recently proposed to construct tractable reformulations for robust static problems that involve profit functions that decompose as a sum of piecewise linear concave expressions. Given that...

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method extends in a natural way a linearization scheme that was recently proposed to construct tractable reformulations for robust static problems involving profit functions that decompose as a sum of piecewise linear concave expressions. Given that th...

The quadratic assignment problem (QAP) is one of the great challenges in combinatorial optimization. Linearization for QAP is to transform the quadratic objective function into a linear one. Numerous QAP linearizations have been proposed, most of which yield mixed integer linear programs (MILP). Kauffmann and Broeckx’s linearization (KBL) is the current smallest one in terms of the number of va...