![]() ![]() ![]() Working paper, SUNY Buffalo, October 2005. In addition to the usual advantages of SOS over MIP for PLO, our SOS approach is more robust than MIP in the sense that it solves PLO even when some of the PLFs are not lower semi-continuous. Here we present a SOS approach for discontinuous PLO that gives the same LP relaxation bound as their MIP models. Recently, Croxton, Gendron, and Magnanti studied three MIP models for discontinuous PLO that are correct when the PLFs are lower semi-continuous, and showed that they give the same LP relaxation bound. It is well established today that the SOS approach is considerably more efficient than MIP for continuous PLO. Later, Beale and Tomlin gave an approach alternative to MIP for continuous PLO based on the concept of special ordered set (SOS). There are many significant applied contexts that require the solution of discontinuous optimization problems in finite dimensions. ![]() They include the incremental cost MIP model of Markowitz and Manne and the convex combination MIP model of Dantzig. Early approaches to piecewise linear optimization (PLO) assumed continuous PLFs. This example fits our intuitive understanding of continuity as well: in order to draw the graph of f(x), we need to. They are also of interest in their own, arising for example in problems with economies of scale. that we call the Michelson continuous piecewise linear differential system.We note that this system is reversible, because it is invariant under the change of variables ((x,y,z,t)mapsto (-x,y,-z,-t)). Piecewise linear functions (PLFs) are commonly used to approximate nonlinear functions. Our goal was to avoid complex, piecewise, discontinuous functions while probing CD gain functions that are consistent with the research literature and with. ![]()
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