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Consider a Geometric Program (GP), $$ \begin{array}{cl} \operatorname{minimize} & f_{0}(x) \\ \text { subject to } & f_{i}(x) \leq 1, \quad i=1, \ldots, m, \\ & g_{i}(x)=1, \quad i=1, \ldots, p, \end{array} $$ where $f_i$ are posynomial functions, $g_i$ are monomials, and $x$ is the optimization variable.

I have problems including the simple equality constraint $Ax - b = 0$, for some $A$ and $b$, into the GP formulation. For example, when I formulate the problem in CVX the problem is not DGP-compliant since this equality violates the disciplined GP rules. This is because standard GPs only allow monomial equality constraints in its formulation, and $Ax - b$ can be interpreted as a posynomial.

Is there any workaround to this? I tried to relax the constraint as $Ax \leq b$ (since polynomials are allowed in inequality constraints) but strangely CVX still raise a DGP error.

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    $\begingroup$ Perhaps a trivial question, but are you sure that the coefficients in A (in your Ax<=b constraint) are positive? $\endgroup$ Jun 24 at 14:51
  • $\begingroup$ @Utkarsh Detha Ding,. ding. ding,, we have a winner. $\endgroup$ Jun 24 at 15:28
  • $\begingroup$ Yes, they actually are positive $\endgroup$
    – Apprentice
    Oct 20 at 5:16

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You might be able to use the suggestions in

https://docs.mosek.com/modeling-cookbook/expo.html#geometric-programming

to convert your problem to a conic optimization problem. It might also make it clear to you the cause of nonconvexity.

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