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[37] | 1 | function [Ax, Ay, b] = bound_exp(xL,xU) |
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| 2 | |
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| 3 | % Two lower bounds from tangents |
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| 4 | % y > exp(xL) + (x-xL)*exp(xL) |
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| 5 | % y > exp(xU) + (x-xU)*exp(xU) |
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| 6 | |
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| 7 | % Upper bound from conneting extreme points |
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| 8 | % y < exp(xU)(x-xL)/(xU-xL) + exp(xL)(xU-x)/(xU-xL) |
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| 9 | |
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| 10 | % can be wrtitten as |
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| 11 | % Ax*x + Ay*y < b |
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| 12 | |
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| 13 | Ay = [-1;-1;1]; |
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| 14 | b = [-exp(xL)+xL*exp(xL); |
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| 15 | -exp(xU)+xU*exp(xU); |
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| 16 | exp(xU)*(-xL)/(xU-xL) + exp(xL)*(xU)/(xU-xL)]; |
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| 17 | Ax = [exp(xL);exp(xU); -exp(xU)/(xU-xL) + exp(xL)/(xU-xL)]; |
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