# Questions tagged [geometric-programming]

For questions related to geometric programming, which considers problems that optimize a posynomial subject to posynomial and monomial constraints.

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### Reason for $\log$ transformation in geometric programming

I have read about the transformation of geometric programs to convex programs. I have read it both in Boyd's book and his geometric programming tutorial. I understand that the transformation indeed ...
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### How to use binary decision variables in Geometric Programming?

I have formulated a MINLP and want to convert into Geometric Programming. There, I want to use binary decision variables. Can someone please guide me that how to declare and use binary decision ...
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### Optimality guarantees of SGD convergence in Geometric Programming

What guarantees of optimality do we get when minimizing with Stochastic Gradient Descent a problem in its original formulation, after showing that it is a Geometric Programming instance (i.e. can be ...
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### Converse to the Duality Theorem of Geometric Programming

The standard method of solving an unconstrained geometric program such as $$\min\left\{g(\mathbf{t}) = \frac{40}{t_1 t_2 t_3} + 20 t_1 t_3 + 10 t_1 t_2 + 40 t_2 t_3 : t_1, t_2, t_3 > 0\right\}$$ is ...
I have an optimization setup where I can represent all objectives/constraints as posynomials. Unfortunately one constraint has the form $g(x) > k$ where $g$ is a posynomial: $$\operatorname{... 2answers 212 views ### In geometric programming, can I maximize a posynomial objective function? A Geometric Programming (GP) problem is given by \min\limits_{x\in R_+^n}f_0(x)\\s.t.\;\;f_i(x)\le 1,i=1,\cdots,p\\\;\;\;\;\;\;\;\;g_j(x)=1,j=1,\cdots,q f_i(x),i=0,1,\cdots,p is a posynomial ... 1answer 59 views ### Can geometric programs be solved more efficiently than general convex optimization problems? I want to solve an optimization problem for which I have already proven that it is feasible and convex. Introducing further variables and considering a special case of the problem, I can formulate it ... 2answers 339 views ### geometric program maximizing using Arithmetic-Geometric mean inequality Maximize xy^2z^3 subject to x^3+y^2+z = 39 and x,y,z > 0. I have that 39 = x^3 + y^2 + z = .. I am unsure what value I should use for \delta_i in each coefficient when using the A-G ... 1answer 1k views ### What is the correct change of variables to yield convexity in this nonlinear optimization problem?$$ \text{min. } x/y \\ \text{s.t. } 2\leq x \leq 3 \\ x^2+y/z\leq \sqrt{y} \\ x/y=z^2 \\ x,y,z\geq 0  To transform this problem into a nonlinear convex optimization problem, both the objective ...
need to find maximum area of rectangle that can be inscribed in a circle of radius r but need to use geometric programming of optimization to this for the maximum area the function is $xy$ (if x ...