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Global Optimization by Bound Contraction

Global Optimization by Bound Contraction - Contraction...

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Global Optimization by Bound Contraction
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Function to Optimize: UB 11 6 minimize O= 4X Y Subject To: 0 X 4 0 Y 8 X Y 4 : -11.6 The optimum can 0.64X Y be visually seen when O= -4X-Y is graphed for varying values of O values of O. From the graph, the upper bound can be found to be at -11.6
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Discretization of a Variable: X
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Now to deal with the issue of Non Convexity Now to deal with the issue of Non Convexity… One of the slices, from x [2,3] Y Z X
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Now to deal with the issue of Non Convexity Now to deal with the issue of Non Convexity… These terms are still non linear Z 4
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From the previous equations the feasible region when
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Fixing the integer × continuous variable nonlinearity Defining: We get the following equations: W d =0 V d =0 Trivial V d =1 Trivial W d =Y
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