# Questions tagged [second-order-cone-programming]

Second-order cone programming (SOCP).

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### Convex constraint for the minimum of a vector

I am solving a second-order cone programming (SOCP) problem. I had to add a constraint that checks if at least one element of the decision variable vector is lower or equal to 0, i.e., I have to add ...
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### Reformulation of Convex Constraints

I am trying to reformulate the constraints $$\alpha^\intercal L \beta + \|L^\intercal \alpha\|_{2}^{2} \leq \rho,$$ where $\alpha\in\mathbb{R}^{n},\beta\in\mathbb{R}^{m}$ and $\rho\in\mathbb{R}$ are ...
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### How can I find the geometric median of n points in 2D Euclidean space using high school level calculus and optimization of total distance?

I am a high school student trying to work on a math project. I have plotted the coordinates of all households in a Kenyan village and am trying to locate the geometric median of the set of points to ...
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### Proving convexity of a second-order cone from basic definition of convexity

I am trying to prove that the second-order cone defined as $C = \{(x,t): || x ||_2 \leq t, t\geq 0\}$ is a cone and is convex. I want to use the definition of convexity. Here is what I have so far: ...
1 vote
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### Is SOCP harder than GP?

As an electrical engineer, I have been studying convex optimization for a while. During my study, I see that most textbooks claim that both second-order cone programs (SOCP) and geometric programs (GP)...
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### Reducing an SDP to an SOCP

Consider a linear estimation setting where we have measurements of the following form. $${\bf y} = {\bf H} {\bf x} + {\bf v}$$ where ${\bf y}, {\bf v} \in \mathbb{R}^m$, ${\bf x} \in \mathbb{R}^n$ ...
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### Trouble visualizing a second-order cone constraint

I have this problem from Boyd's optimization textbook: A standard form for the SOCP model is $$\text{minimize } f^Tx \\\text{subject to: }‖A_ix+b_i‖_2 ≤ c_i^Tx + d_i, i= 1,\dots,m$$ where we see ...
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I'm new to convex analysis and got stuck when formulating a dual problem for a rotated conic programming problem. The problem is as follows. $\min \ \ 2x_1+2x_2+x_3-3x_4$ $s.t. \ \ x_1 \leq 7$ \$ ...