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Questions tagged [cvx]

a MATLAB-based modeling framework for convex optimization.

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0answers
72 views

Best optimizer for unconnstrained non-convex nonlinear least-square optimization problem?

I am looking for a very good optimizer to the following problem: $$\min_{P,\Theta}\lVert APD(\Theta)P^{-1} -B \rVert_F$$ where $A,B \in \mathbb{R}^{n\times m}$, $P \in \mathbb{R}^{m\times m}$, $D\in \...
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1answer
59 views

Formulate and solve a simple conic programs in cvxpy language [closed]

Let $r,\epsilon > 0$ and $a, b \in \mathbb R^n$ with $\|a\|_2 \le r$. Define $C(a) := \{x \in \mathbb R^p | \|x+a\|_2 \le r,\;\|x\|_\infty \le \epsilon\}$, and assume it is non-empty. Question (A)...
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2answers
5k views

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 ...
7
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5answers
3k views

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 ...
1
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0answers
216 views

Sign or cardinality constraint when solving for sparse signal

I'm currently learning about using linear and semidefinite programming to find sparse solutions to problems. In particular, finding sparse solutions where the sampling functions are sinusoidal (...
1
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1answer
198 views

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 $\eta$ ...
1
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2answers
356 views

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 ...
0
votes
1answer
522 views

Positive definite matrix in CVX

I'm trying to use CVX to solve SDP problem. I have a constraint with positive definite matrix, but if i read the document of CVX, I can only find variable with positive semidefinite matrix. Can anyone ...
1
vote
1answer
736 views

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: ...
3
votes
1answer
1k views

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 ...
5
votes
1answer
578 views

Semidefinite Programming Using CVX in Matlab

I have the following optimization problem $$\begin{align} &\min_{ X_{1}, \dots,X_{k} } \max_{ \theta, \phi } \left|P_{d}(\theta,\phi) - \sum_{k=1}^K \operatorname{Tr}(a_{k}(\theta,\phi)a_{k}^{H}...
0
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1answer
2k views

How do I correctly multiply vectors and matrices in Python and MATLAB?

I have been trying for 2-3 days now to get L2 regularized logistric regression to work in Matlab (CVX) and Python(CVXPY) but no success. I am fairly new to convex optimization so I am quite frustrated....
0
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1answer
98 views

CVX : Obtaining the minimizing parameter at the optimum

In CVX, how do we return the value of the parameter over which the problem is minimized at the optimal value? By this, I mean, how do we obtain $$x^* = \arg\min_x f(x)$$ when solving the problem ...
1
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0answers
156 views

Coding a convex problem in CVX

I am new to CVX and am trying to simulate this convex problem I found in a paper. $$\min_{\gamma,\mathbf{mu},\mathbf{G},\mathbf{\Omega},t} \text{Tr}(\mathbf{G}\mathbf{C}\mathbf{G}^H)+t \\ s.t. -t-\...
2
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1answer
2k views

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: ...
1
vote
2answers
543 views

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 ...
0
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3answers
524 views

Solving rank deficient systems with cvx

I am using cvx to solve linear programs with constraints of the form $Ax=b,x\ge0$. However the matrix $A$ is rank deficient and cvx returns a warning and finally displays status as 'Infeasible'. Rank ...
0
votes
1answer
395 views

Custom CVX Functions - Overriding Errors [closed]

I have constructed a function in Matlab that is convex and increasing (qualitatively similar to an exponential function but I am hoping to avoid the successive approximation requirement of exp). In my ...
1
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0answers
82 views

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 ...
3
votes
2answers
843 views

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 ...