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 ...
user2987's user avatar
  • 193
5 votes
1 answer
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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}...
user3100463's user avatar
4 votes
2 answers
7k 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 ...
syli's user avatar
  • 41
4 votes
1 answer
170 views

How to form the following constraint in cvx?

The optimization problem is $$\min_{x\in K} \|h - x\|_2$$ where $$K = \{v\in R^n : \exists \lambda \geq 0\ v_1=v_2=\ldots=v_k=\lambda \ \text{and} \ |v_i| \leq \lambda \ \text{for} \ i=k+1,\ldots,n \...
Bihu Duo's user avatar
  • 143
3 votes
2 answers
1k 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 ...
Fede_v's user avatar
  • 33
3 votes
1 answer
2k 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 ...
jd98's user avatar
  • 31
3 votes
1 answer
115 views

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 ...
Lee's user avatar
  • 183
2 votes
1 answer
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Convex optimization: what is atom library?

By reading the CVX users' guide, I frequently came across with the term "atom library", which I suppose to be a set of functions that one must use to construct mathematical expressions on ...
Rubem Pacelli's user avatar
2 votes
1 answer
110 views

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 ...
Mini's user avatar
  • 123
2 votes
1 answer
4k 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: ...
lihong peng's user avatar
2 votes
1 answer
178 views

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]\\ &\...
fengbiqian's user avatar
1 vote
1 answer
2k 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: ...
tian qing's user avatar
1 vote
1 answer
525 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 $\eta$ ...
MarsPlus's user avatar
  • 113
1 vote
2 answers
622 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 ...
Excalibur's user avatar
  • 113
1 vote
2 answers
488 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 ...
Rob's user avatar
  • 143
1 vote
0 answers
272 views

Problem in parameterizing a CVXPY program

I am trying to parameterize a CVXPY program as I need to repeatedly solve the problem, but I noticed that when my parameters are complex numbers, CVXPY models the problem in each iteration. For ...
Nash J.'s user avatar
  • 111
1 vote
0 answers
397 views

Why is the problem infeasible?

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}} & ...
fengbiqian's user avatar
1 vote
0 answers
97 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 \...
ArtificiallyIntelligent's user avatar
1 vote
0 answers
163 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-\...
Karthik Upadhya's user avatar
1 vote
0 answers
86 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 ...
user34790's user avatar
  • 473
1 vote
0 answers
231 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 (...
geometrikal's user avatar
0 votes
1 answer
3k 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....
Behroz Sikander's user avatar
0 votes
3 answers
679 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 ...
Pawan Aurora's user avatar
0 votes
1 answer
94 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)...
dohmatob's user avatar
  • 175
0 votes
1 answer
1k 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 ...
pippp's user avatar
  • 103
0 votes
1 answer
207 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 ...
Karthik Upadhya's user avatar
0 votes
1 answer
428 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 ...
Erik M's user avatar
  • 103
0 votes
1 answer
429 views

Why is a elementwise max not DCP?

I am trying to formulate a convex optimization problem using CVXPY. Everything works, except a constraint that does not seem to follow DCP rules. Let $D \in \Bbb R^n$ be a decision variable and let $Q$...
Sahil Gupta's user avatar
0 votes
0 answers
207 views

Absolute value constraint in quadratic programming optimization

$$ argmin(x,y)=x^2+y^2+2y $$ $$ s.t.\ \ y=|x-10| $$ How can I convert the absolute value constraint to the constraint matrix (GX<=h, AX=b) in cvxopt?
lichgo's user avatar
  • 109
0 votes
0 answers
144 views

CVXOPT intermediate step valuation stepping out of function domain of defintion

I am using CVXOPT, particularly to solve a nonlinear convex optimization problem. Either the objective function or the constraints involve some functions that are only defined in a strict subset of $\...
Hans's user avatar
  • 121