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Questions tagged [socp]

For questions related to second-order cone programming, a type of convex optimization problem.

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3 votes
0 answers
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Is the following constraint a second-order cone constraint?

We all know that the following constraint is called second-order cone constraint $$ \|Ax + b\|_2 \leq c^T x + d $$ where $x \in \mathbb{R}^n$, $A \in \mathbb{R}^{(k-1) \times n}$, $b \in \mathbb{R}^{k-...
Kaiming Zhang's user avatar
1 vote
1 answer
64 views

Linearizing a quadratic constraint

I am working on a quadratic conic optimization problem, but I have discovered that it would be preferable if the quadratic constraint is linearly approximated. In other words, I need some way to make ...
Mikkel Honningsvåg Sandhaug's user avatar
0 votes
1 answer
76 views

Dual of second order cone programming with both equality and inequality constraints

How to derive the dual of a second order cone programming with both equality and inequality constraints? Here is the optimization problem I want to handle: $$ \begin{array}{rl}\min_{\mathbf{x},\mathbf{...
Kaiming Zhang's user avatar
2 votes
1 answer
81 views

epigraphs for quadratic constraints

I have a constraint of the following form \begin{equation} x^{\top}x + y^{\top}y \leq t \end{equation} where x, y are vector variables and t is a scalar variable. I can augment the variables x and y, ...
Kumar's user avatar
  • 153
5 votes
1 answer
487 views

How to formulate the inequality constraint $\sqrt{x^2+y^2} \leq z$ using gurobipy?

How to formulate the following constraint using gurobipy $$ \sqrt{x^2 + y^2} \le z$$ where $x, y, z$ are continuous optimization variables? I saw how to formulate it using CVXPY: ...
Hussein Sharadga's user avatar
8 votes
1 answer
502 views

Solving maximization problem with linear-fractional sum

I want to solve this problem : Maximize \begin{equation} \sum_{i=1}^{n} \frac{x_i}{a_ix_i + b_i}\end{equation} with the constraints \begin{equation}\sum_{i=1}^{n}x_i = S \ , \ x_i \geq 0 \ \forall \ ...
ghiloka's user avatar
  • 83
5 votes
2 answers
422 views

Quadratically constrained convex optimization

I have tried to convert the following constraint into SOCP form but can't figure it out. My issue is that whenever I create the norm, the other side has to be square rooted which invalidates the SOCP ...
Mosab Qaissiah's user avatar
2 votes
1 answer
459 views

Hyperbolic constraint as second-order cone

I have a problem which simplifies to: $$ \begin{align} \max w &\\ w&\le xy \\ x,y&\le10 \\ x,y&\ge0 \end{align} $$ Recognizing that $xy$ form a hyperbolic constraint, I can solve by ...
Richard's user avatar
  • 543