CVX is a popular modeling framework for disciplined convex programming that CVX turns MATLAB into a modeling language, allowing constraints and objectives to be specified using standard MATLAB expression syntax.
Questions tagged [cvx]
43 questions
3
votes
2 answers
Minimize $\|AXBd -c \|^2$, enforcing $X$ to be a diagonal block matrix
Currently, I am minimizing the quadratic objective $\|\mathbf{A}\mathbf{X}\mathbf{B}\mathbf{d} -\mathbf{c} \|^2$ using CVX, as follows
echo on
cvx_begin
variable xx(num_triangles*3,num_triangles*3)
minimize( norm( A * xx * B * d - c )…
Dan
- 153
3
votes
1 answer
Low rank approximation using CVX toolbox in Matlab
I try to use CVX toolbox to do "low rank approximation" work. The code is as follows:
r = 2; % the rank;
N = 32; % the dimension
M = 32;
a = randn(N,r);
b = randn(M,r);
X = a*b'; % low rank Matrix;
A = rand(20,N);
Y = A*X;
% low rank approximation…
cvxfan
- 31
2
votes
0 answers
How to check the feasibility of standard LMI using Matlab/CVX?
In the wikipedia page of LMI, the standard form is given by
$$A_0+y_1A_1+y_2A_2+\cdots+y_mA_m \succeq 0,$$
where $A_i$ are $m\times m$ symmetric matrices and $y_i$ are real vectors, $i=1,2,\ldots m.$
I have few problems in this LMI standard form…
Lee
- 1,978
2
votes
1 answer
How do I implement this convex quadratic-linear function in CVX?
From Proving that quadratic form is convex in (vector, matrix) arguments we know that $$f(Q,x) = x^T Q x$$ is a convex function jointly in $Q$ and $x$ when $Q\succeq 0$. How can I optimize with respect to this in CVX?
Supposedly, trace_inv is…
Paul Zhang
- 109
2
votes
0 answers
Standardizing a convex problem
Consider the following convex optimization problem
\begin{align}
\max_{\mathbf{X},\mathbf{v}}~&~\mbox{trace}(\mathbf{QX}) \\s.t.&~~\mbox{diag}(\mathbf{v})-\mathbf{X}\succeq 0 \\ &~~ \mathbf{X} \succeq 0,~~\mathbf{e}^T…
dineshdileep
- 9,113
2
votes
1 answer
Finding the maximum volume inscribed ellipsoid using CVX
I am trying to use the CVX package in Matlab to find the largest inscribed ellipsoid for a convex set of points. I was also able to get the example from this link running.
[Step 1] This is how the optimization problem is formulated in the sample…
optimum_Jay
- 68
2
votes
1 answer
Maximizing $\frac{ax}{cx+d}$ over $[0,1]$ using CVX
I have the following concave function
$$f(x)=\frac{ax}{cx+d}$$
where $a, c, d > 0$ and $0 \le x \le 1$. How can I use CVX tools to maximize $f(x)$?
It seems that the CVX does not support such structure even if $f(x)$ is concave.
Dave
- 606
2
votes
3 answers
Optimal Distribution of Proctors
In my university, I am responsible with the distribution of proctors with respect to the student placements to the classrooms in freshman math pool courses. I faced a problem which is sticked in my mind for a quite long time. The problem is to…
Gökhan Göksu
- 118
2
votes
2 answers
Maximizing a convex quadratic function in CVX and Matlab
I understand that a convex function can not be maximized as there is no such value. However, consider the following function:
$$\begin{array}{ll} \text{maximize} & 3x^2 + 5y^2\\ \text{subject to} & x+y=12\\ & x,y\geq0\end{array}$$
But executing it…
1
vote
1 answer
Matlab Optimization Toolbox versus CVX?
I would like to know what the difference between the Matlab Optimization Toolbox and CVX, which is a convex optimization toolbox? Can a convex optimization problem be solved in both?
HHH
- 247
1
vote
0 answers
Getting concave function accepted by CVX
Part of my problem is maximizing the minimum magnitude squared of vector elements (x = [x_i]). This is not a convex problem as min is taking convex expressions.
One way to work with it is by maximizing g = log_prod(d(x)), where d=[d_i] and d_i =…
Aya
- 11
1
vote
1 answer
Solving a convex problem with quasiconvexity with CVXPY?
I have a question regarding quasiconvexity and its usage in CVXPY.
I have the following optimization problem.
\begin{equation*}
\begin{aligned}
\min_{x} \quad & \sqrt x\\
\textrm{subject to:} \quad & 1 \leq x \leq…
Michael
- 53
1
vote
1 answer
Formulating constraints in CVX — exercise 4.3(d) of Additional Exercises for Convex Optimization
I am trying to solve exercise 4.3(d) of the Additional Exercises for Convex Optimization. In this exercise, it is asked to express the following constraint in CVX, using the rules for disciplined convex programming (DCP).
$$
x + z \leq 1 + \sqrt{xy…
tigre200
- 225
1
vote
0 answers
Issues with CVX package for optimization
I am trying to use the cvx package for optimization. However, I am having some issues with it. I have a variable $X$ which is a matrix but I cannot add $X^{-1}$ in the objective function. What should I do? Is it even possible to use it or it…
user34790
- 4,412
1
vote
0 answers
Maximize sum of gamma cumulative distributions as disciplined quasiconvex problem (DQCP) in CVXPY
Is is possible to formulate the maximization of the sum of gamma cumulative distributions as a disciplined quasiconvex problem (DQCP) in CVXPY?
I'm trying to solve the following problem:
Given $F(x) = \int_0^x t^{\alpha-1}exp(-t) dt$ (proportional…
gnarls
- 35