Questions tagged [second-order-cone-programming]
Second-order cone programming (SOCP).
107 questions
0 votes
3 answers
216 views
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
0 votes
1 answer
53 views
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
0 votes
1 answer
65 views
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 vote
1 answer
91 views
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
0 votes
1 answer
114 views
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 ...
0 votes
1 answer
54 views
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 vote
0 answers
47 views
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 votes
1 answer
186 views
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 vote
0 answers
35 views
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
1 vote
1 answer
194 views
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
0 votes
0 answers
44 views
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 votes
1 answer
434 views
reduction from QCQP to SOCP
Suppose a QCQP problem : $$ \min_{x\in\mathbb{R}^{n}}f\left(x\right)=\frac{1}{2}x^{T}P_{0}x+q_{0}^{T}x$$ $$ s.t:\begin{cases} \frac{1}{2}x^{T}P_{i}x+q_{i}^{T}x+r_{i}\le0 & i=1,2\dots,m:m\le n \...
- 927
2 votes
1 answer
49 views
Convex constraint for the minimum of a vector
I am solving a second-order cone programming (SOCP) problem. I had to add a constraint that checks if at least one element of the decision variable vector is lower or equal to 0, i.e., I have to add ...
- 107
0 votes
1 answer
98 views
Reformulation of Convex Constraints
I am trying to reformulate the constraints $$ \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
2 votes
2 answers
242 views
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 ($...
