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The proposed nonlinear relaxation is used to reformulate the GDP problem as a tight MINLP problem, and for deriving a branch and bound method.
The model is formulated as a Generalized Disjunctive Programming (GDP) problem and solved using the logic based outer approximation algorithm without MINLP reformulation.
The method relies on converting the GDP problem into an equivalent big-M reformulation that is successively strengthened by cuts generated from an LP or QP separation problem.
In this paper, we describe a new convex nonlinear relaxation of the nonlinear GDP problem that relies on the use of the convex hull of each of the disjunctions involving nonlinear inequalities.
Through defining logical variables that indicate the relative temperature positions of refrigerant streams after sub-coolers, the synthesis is formulated as a Generalized Disjunctive Programming (GDP) problem based on LP transshipment model, with the target of minimizing the total compressor shaft work in the refrigeration system.
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The GDP problems are converted into mixed-integer form using the big-M approach.
Computers and Chemical Engineering, 24, 2125 2141] have developed a reformulation for nonlinear Generalized Disjunctive Programming (GDP) problems that obtains from the intersection of the convex hulls of every disjunction.
Computers and Chemical Engineering, 24, 2125 2141] have developed a reformulation of Generalized Disjunctive Programming (GDP) problems that is based on determining the convex hull of each disjunction.
In order to circumvent this issue, a cutting plane method that can be applied to linear GDP problems is proposed in this paper.
In health care (17% of GDP), the problems of asymmetric information and moral hazard mean that increased spending results in little or no improvement in health outcomes.
The most oft-cited measure, gross debt levels approaching 170% of GDP, overstates the problem, since it does not account for financial assets held by the government.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com