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I am a post graduate student in Electrical Engineering and I am working in optimization. Suddenly, I was running into a situation where my problem has a constraint in the form of

$${x_1}{x_2}{x_3} - \left( {\frac{1}{3}{{\left( {{x_1}} \right)}^3} + \frac{1}{3}{{\left( {{x_2}} \right)}^3} + \frac{1}{3}{{\left( {{x_2}} \right)}^3}} \right) \le 0$$

From what I learn about signomial programming the signomial constraint should look like

enter image description here

$${x_1}{x_2}{x_3} - \left[ {\frac{1}{3}{{\left( {{x_1}} \right)}^3} + \frac{1}{3}{{\left( {{x_2}} \right)}^3} + \frac{1}{3}{{\left( {{x_2}} \right)}^3}} \right] \le 1$$

However, there is no $1$ on the right hand sign of my problem. How can I circumvent this ?

As a follow up question, I want to know if signomial programming can be solved efficiently like the usual convex optimization problem ?

Thank you very much !

Rodrigo de Azevedo
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Tuong Nguyen Minh
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1 Answers1

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You can simplify your constraint by using this formula $$x_1^3 +x_2^3 +x_3^3 -3x_1x_2x_3 = (x_1+x_2+x_3)(x_1^2+x_2^2+x_3^2-x_1x_2-x_2x_3-x_3x_1)$$ Then the constraint becomes $$x_1+x_2+x_3 \ge 0$$

NN2
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