# Questions tagged [convex-optimization]

Convex Optimization is a special case of mathematical optimization where the feasible region is convex and the objective is to either minimize a convex function or maximize a concave function.

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### 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 $Q$...
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### 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?
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### How do I find the minimum-area ellipse that encloses a set of points?

I have a set of points that resembles more of an ellipse than a circle. I implemented the optimization formulation below and the solution gives a circle. I tried with various initial values, still to ...
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### Formulating this optimization problem

Suppose I want to minimize below objective function $\sum | g(x_i) \cdot I_{g(x_i)<0} |^2$ i.e, the latter penalty terms like $|g(x_i)|^2$ are only computed when $g(x_i)<0$. $|g(x_i)|^2$ are ...
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### Comparing minimas of two different functions

The goal is to find vectors $x_u$ and $y_i$, both of the same length $f=64$, and to do this the following loss function is minimized: $$\sum_{u, i} (1 + \alpha \cdot r_{ui})(p_{ui} - x_{u}^{T}y_i)^2$$ ...
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### successive convex approximation and Convergence

In successive convex approximation method, can the solution be considered to be an acceptable solution if the algorithm reaches the maximum number of iterations without noticeable convergence? or it ...
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### Expressing a Constraint in an optimization problem

If I have a vector of M "continuous" decision variables (say it is called x) , and if I want a constraint to express that only one of them is allowed to have a nonzero value (i.e. no more ...
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### Optimization problem

In the expression: $${\underset{\Omega}{\min}\left\|\beta A\Omega^{-1}B+C\right\|_{F}^{2}}\, ,$$ $$\text{subject to tr}(\Omega)=1, \Omega \ge 0\, ,$$ where ${\Omega}$ is nonnegative and symmetric ...
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### Efficient solver of a Integer programming

I am solving an Integer programming using MATLAB, yet the efficiency is low. Here is the problem: Suppose $v$ is a $N \times 1$ vector. For $v_i \in v$, $v_i \in \{0,1\}$. $D$ is a 0-1 matrix, which ...
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• 121
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### L2 norm optimization problem

I have an optimization problem where i need to find an image x, that is very close to x' such that: monitor(x') is valid but monitor(x) is invalid. (output is valid when the neural network output is ...
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• 1,331
1 vote
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• 121
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### log(det(X)) in Semidefinite Programming

I have been solving problems of the form $$max \ log(det(A)) \\ s.t. \ A = A^{T} \succeq 0, \\ p_{i}^{T}Ap_{i} \leq b_{i}$$ where $b_{i}$ and $p_{i}$ are input vectors (to be clear there is more than ...
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### Underdetermined Minimum Volume Enclosing Ellipsoid

Given three vectors in $\mathbb{R}^{512}$, my task is to compute a Minimum Volume Enclosing Ellipsoid (MVEE). I have tried Kachiyan's algorithm, but it requires at least as many vectors as there are ...
1 vote
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### In which cases does the nonlinear conjugate gradient method take more than $n$ steps?

I have programmed a couple of Matlab implementations of nonlinear Conjugate Gradient methods (Fletcher Reeves and Polak Ribeire). However, I am concerned with how many steps it's taking to optimise ...
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### Proving convexity of Frobenius norm and correlation function formulations of an optimization problem

I have been working on formulating my requirements in the form of an optimization problem in a multi-output regression setting. Firstly, I would like to make the variables I used in the problem and ...
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### Interior point of convex polytope

Suppose the convex polytope is the set of feasible solutions $\mathbf{x}\in\mathbb{R}^n$ for the linear system $\mathbf{A}\mathbf{x}=\mathbf{b}\,,\; \mathbf{A}\in\mathbb{R}^{m\times n}$ subject to ...
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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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1 vote
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### A maximization problem, with motivation in machine learning

Consider the minimization problem described this paper. Let $f_{\lambda}$ be the minimizer. As a part of extending my work, I am able to show the following facts \lim_\limits{\lambda \to 0}\|f_{\...
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### Geometric Programming - symbolic version

I am interested in finding minimizers of functionals of the type $\sum x^ay^bz^c$ where the exponents are 1, 0 or -1. I have codes to find such minimizers when they exist up to machine precision, ...
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### Convexity of Sum of $k$-smallest Eigenvalue
If I have a real positive definite matrix $A\in\mathbb{R}^{n\times n}$, and denote its eigenvalues as $\lambda_1\leq \lambda_2 \leq ... \leq \lambda_n$. Define the function as \$f(A)=\sum_{i=1}^{k} \...