# Geometric Programming with Simple Affine Equality Constraint

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.

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