Abstract
This paper addresses itself to the algorithm for minimizing the sum of a convex function and a product of two linear functions over a polytope. It is shown that this nonconvex minimization problem can be solved by solving a sequence of convex programming problems. The basic idea of this algorithm is to embed the original problem into a problem in higher dimension and apply a parametric programming (path following) approach. Also it is shown that the same idea can be applied to a generalized linear fractional programming problem whose objective function is the sum of a convex function and a linear fractional function.
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Konno, H., Kuno, T. Generalized linear multiplicative and fractional programming. Ann Oper Res 25, 147–161 (1990). https://doi.org/10.1007/BF02283691
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DOI: https://doi.org/10.1007/BF02283691