Questions tagged [second-order-cone-programming]
Second-order cone programming (SOCP).
107 questions
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How do I find the straightest path through 3D rectangles?
I'm mainly a programmer, not a mathematician, so please bear with me.
I have a sequence of rectangles in 3D space. Each one has a specified pose: position, an orientation (rotation in 3D), and a width ...
- 111
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1
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53
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SOCP standard form
I have the following concave optimization problem
$$\max_x \; c^\top x - \sum_{i=1}^n \left( \lvert x_i \rvert + \lvert x_i \rvert^{3/2} \right) $$
I am able to solve it numerically using SOCP solvers,...
- 1,510
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62
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Solve Second Order Cone Constraint
I am trying to solve the following second order cone constraint in Python (gurobipy), but it doesn’t recognize it as a SOC. Could anyone help me how to code it?:
\begin{equation}
- \left(\sum_{\tau=1}...
1
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1
answer
88
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Projection onto a generic second-order cone
I am looking for an analytical formulation of the projection of a generic vector $\mathbf{v}\in\mathbb{R}^3$ onto the second-order cone $\|\mathbf{x}\|\le\mathbf{c}^T\mathbf{x}$. While I was able to ...
- 107
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What Optimization Methods Are Suitable for Solving This Problem? [closed]
am new to the field of optimization and have encountered the following optimization problem. I am curious to know what type of optimization problem this is and what methods are appropriate for solving ...
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53
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Optimize a convex difference of quad forms
I have an optimisation problem of the form:
$$\min_x c^T x + \| V x\|^2_2 + \| D x\|^2_2 - \| W x\|^2_2$$
Subject to linear constraints.
$D$ is diagonal and $V$, $W$ are non-square matrices. I know ...
1
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0
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46
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Is there an SOCP presentation of power of non-convex term for this constraint $\frac{1}{4}{\left( {1 + xyz} \right)^2} \le t$?
I am a network engineer who is currently working with some network optimization problem. In my problem the term $\frac{1}{4}{\left( {1 + xyz} \right)^2}$ appears on the objective function and I can ...
2
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1
answer
185
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Optimization problem with two (inequality) constraints
I am trying to solve the following optimization problem:
$\begin{align}\min_{\mathbf{c}_{k}} \sum_{k=1}^{K}\frac{q_k}{c_k} \\
\text{s.t. } c_k &\geq t_k \tag1\label1 \\
\sum_{k=1}^{K} c_k &\...
1
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0
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Minimization of smooth objective with conic constraint
I am interested in deriving first-order optimality conditions for
\begin{equation}
\min_{x\in\mathbb{R}^{n}}f(x)\\
\text{s.t. }x\in\mathcal{K}
\end{equation}
where $f$ is a smooth function and $\...
- 2,100
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Simple examples of conic programming and second order cone programming [closed]
I was looking at the book LECTURES ON MODERN CONVEX OPTIMIZATION, by Ben-Tal and Nemirovski, which covers a lot of material on conic optimization or conic programming. The ideas I seem to get, but I ...
- 2,705
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Can geometric programming be considered as a special case of second order cone programming?
From the Mosek cookbook, it is clear that by using the log-sum-exp transformation and some extra variable $u_k$, a geometric programing problem can be transform into a exponential cone presentation.
...
3
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1
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430
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reduction from QCQP to SOCP
Suppose a QCQP problem :
$$ \min_{x\in\mathbb{R}^{n}}f\left(x\right)=\frac{1}{2}x^{T}P_{0}x+q_{0}^{T}x$$
$$ s.t:\begin{cases}
\frac{1}{2}x^{T}P_{i}x+q_{i}^{T}x+r_{i}\le0 & i=1,2\dots,m:m\le n
\...
- 927
2
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1
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Convex constraint for the minimum of a vector
I am solving a second-order cone programming (SOCP) problem. I had to add a constraint that checks if at least one element of the decision variable vector is lower or equal to 0, i.e., I have to add ...
- 107
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Reformulation of Convex Constraints
I am trying to reformulate the constraints
$$
\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 ...
- 334
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Proof regarding center of an optimal Euclidean ball containing distinct points
Suppose we are given $k$ distinct points $a_i \in \mathbb{R}^n$ for $i = 1, 2, \dots, k$, and our objective is to determine the Euclidean ball with the smallest radius that contains all these points ($...
