# Questions tagged [cvx]

a MATLAB-based modeling framework for convex optimization.

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### Minimizing $\mathrm{trace}(S)+\mathrm{trace}(S^{-2})$ using CVX

In Matlab, I would like to minimize the function $$f(S)=\mathrm{trace}(S)+\mathrm{trace}(S^{-2})$$ where $S \in \mathcal{M}_{m,m}$ is symmetric and positive definite, which is definitely a convex ...
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### how can a 2-d fft be constructed to an equivalent matrix?

When I use the cvx matlab toolbox, I met a puzzled problem. The function of fft (or dct, wavelet, etc.) cannot be recognized by the type of 'cvx'. For the 1-d fft, it can be constructed to an ...
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### Finding A and X such that AX = 0, X is positive non-zero, and A is sparse

I apologize if this is a naive question. I'm trying to create some boostrap data for a system of linear, ordinary differential equations at steady state. Since the equations represent the ...
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### How can I minimize the number of non-zero elements in the solution vector subject to linear constraints (MATLAB)?

all, I've tried to find an answer to this question and have come across some related threads but nothing I was able to apply to my problem given my relative lack of experience in this arena. I ...
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### Find $x$ that satisfy $(I-A^*A)+x(\frac{A+A^*}{2})\prec0$ using LMI or SDP on Matlab

Given $A\in\mathbb{C}^{n\times n}$, I want to use LMI or SDP to find feasibility of $x>0$ in the following inequality: $$(I-A^*A)+x(\frac{A+A^*}{2})\prec0,$$ where $D\prec0$ means that $D$ is ...
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### A concave maximization that is not supported on CVX

I try to solve a maximization problem using CVX. In its simplest form, I want to maximize $$f(x,y)=y*h_b\left(\frac{x}{y}\right),$$ where $h_b(\cdot)$ is the binary entropy function. In the context ...
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### Disciplined convex programming error: Only scalar quadratic forms can be specified in MATLAB's CVX

I want to minimize $$W\, \text{tr}\left([A-Y_{pie}][A-Y_{pie}]^T\right) + \lambda\Vert A\Vert\, \enspace ,$$ however, I encounter the following problem: ...
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### Could the convex problem be tackled by CVX?

I want to solve the convex optimization as follows: \begin{align} \underset{X_1,X_2}{\min} &\ -\frac{1}{N}\sum_{i=1}^N\log\det\left(I+H_i^HX_2H_i\right)-\log\left[1+h^H(X_1+X_2)h\right]\\ &\...
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### Matrix transpose multiplication

In CVX, I encounter a problem. I want to multiply a Matrix of 2x4 with its transpose. I know the result must be positive definite. However, it couldn't let me do the multiplication directly. Says: ...
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### How to deal with quadratic constrain in semidefinite programming

I am using CVX to solve an optimization problem. One of my constraints in the problem is $$M \succeq \eta {\eta}^T$$ where $M$ is a square matrix and $\eta$ is a column vector (both $M$ and $\eta$ ...
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### How to represent weighted nuclear norm of matrix variable X and minimize it by CVX function, or solve it by other possible packages

I want to minimize $f(x) = \mathrm{Tr}(\sqrt{\mathbf{X}^{T}\mathbf{X}}\mathbf{A})$, where $\mathbf{X}$ is an matrix variable of dimension $d \times d$, and $\mathbf{A}$ is a known matrix. I tried the ...
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### How to nest 2 simple CVX problems? Is it possible at all?

I have the underdetermined outer optimization problem $$\text{min}_{x\geq 0}\quad \|Ax-b_1\|_2^2+\|AT(x)-b_2\|_2^2$$ with $A\in\mathbb{R}^{m\times n}$ and $m<<n=64^2$ or in corresponding CVX ...
Given $\mathbf V_t=\mathbf v_t\mathbf v_t^H$ where $\mathbf v_t=\left(e^{j\theta_{1}},e^{j\theta_{2}}\right)^H$: \begin{equation*} \begin{array}{ll} \underset{\mathbf V}{\operatorname{minimize}} & ...