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Introduction Ax b GAMS A - Amsterdam Optimization

SOLVING SYSTEMS OF LINEAR EQUATIONS WITH GAMSERWIN document describes some issues with respect to solving sys-tems of linear equationsAx=busing a system of linear equationsAx=b, whereAis a (square) matrix, is ataskGAMSand LP solvers are well equipped to do. As LP solvers do not requireAto be square, even more general systems can be solved. Even if the matrixAissingular, an LP solver will report a solution, provided there exists a trick that needs to be used to shoe horn such a model into a linear opti-mization model is to select a variable to optimize. One can just pick a variable thatappears in the model, especially when it is known that there exists just one uniquesolution. However, from a modeling point of view it may be better to introduce adummyvariable. This makes clear that this variable has no intrinsic meaning inthe model, but just is created for syntactical reasons. Below is a small example ofa system of linear equations that is not square.

SOLVING SYSTEMS OF LINEAR EQUATIONS WITH GAMS ERWIN KALVELAGEN Abstract. This document describes some issues with respect to solving sys-tems of linear equations …

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