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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1answer
53 views

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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1answer
17 views

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 ...
0
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1answer
105 views

Perspective of log-sum-exp as exponential cone

According to the Mosek documentation, Geometric Programming constraints of form log-sum-exp can be formulated with exponential cones. If the constraint is of form $$t \geq \log(\exp(x_1)+\ldots + \...
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1answer
100 views

Solving an optimization problem with lower computational complexity

Given $$n, C, r_i, p_i, \quad∀ i={1,2,...,n} $$ I want to solve this optimization problem: $$maximize \quad f(x_1,x_2,...,x_n)=\prod_{i=1}^n {{(x_i/r_i)}^{p_i}} $$ $$s.t \quad {(x_i/r_i)≤1}, \quad {(\...
2
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0answers
69 views

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 ...
5
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1answer
326 views

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 ...
0
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1answer
71 views

Geometric program with posynomial > 1

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{...
0
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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 ...
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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 ...
0
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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 ...
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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 ...
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2answers
5k views

maximum area of rectangle inscribed in a circle using geometric programming

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 ...