All Questions
Tagged with convex-optimization disciplined-convex-programming
16 questions
8
votes
4
answers
575
views
Disciplined convex programming representation of $x\sqrt{1-x}$
Anyone have an idea for a disciplined convex programming (DCP) representation of the concave function $x\sqrt{1-x}$, which is defined over the domain $[0,1]$?
The Taylor series about $x=0$ is $$x - \...
8
votes
1
answer
294
views
Distributed optimization problem
Consider the following optimization problem:
\begin{equation}
\label{eq:1}
\min_{x\in\mathcal X} \max_{i\in\mathcal I}\sum_{j\in\mathcal J} f_i(x_{(j)}),
\end{equation}
where $\mathcal{I}$ and $\...
- 215
5
votes
1
answer
237
views
Constraints like "max(column a + column b) == 2" are not DCP
I am struggling with the following constraint on a minimization problem
cvx.max(z[:, i] + z[:, j]) == 2
where z is a Boolean ...
- 970
5
votes
2
answers
184
views
Global optimizers handling minimization of expressions like $\log{v}+\frac{1}{v}$
Consider the simple problem of maximum likelihood estimation of the variance of a mean zero normal distribution. The expression to be minimised is:
$$N \log{v}+\frac{1}{v}\sum_{n=1}^N{b_n^2},$$
where $...
- 269
5
votes
1
answer
587
views
How to formulate the inequality constraint $\sqrt{x^2+y^2} \leq z$ using gurobipy?
How to formulate the following constraint using gurobipy
$$ \sqrt{x^2 + y^2} \le z$$
where $x, y, z$ are continuous optimization variables?
I saw how to formulate it using CVXPY:
...
- 409
4
votes
1
answer
167
views
DCP formulation of sum of nonconvex and convex functions
I am trying to find a DCP formulation for the following convex objective function (using CVXPY):
Let $x$ be the $N$-dimensional vector variable on which we optimize on, $c$ be a known scalar value ...
- 41
3
votes
1
answer
350
views
Express equality constraint involving exponentials cones
The exponential cone is define such that
$(x, y, z) \in \text{ExpCone: if } y \exp(x / y) \leq z \land y > 0.$ The inequality $\exp(a) \leq b$ can be expressed as $[a, 1, b] \in \text{ExpCone}$.
...
- 4,049
3
votes
2
answers
270
views
DCP representation of a convex quotient of affine functions
I am trying to represent the following inequality:
$$\frac{x}{1-x} \leq y \qquad\mathrm{with}\qquad 0<x<1$$
The function on the left is convex (its second derivative is always positive over ...
- 1,008
3
votes
1
answer
547
views
Adding CVXPY abs to optimization problem turns out to be non-DCP
I have tried to solve an optimization problem using CVXPY library. This problem aims to minimize the distance between a vector of $n$ variables ($\beta$), which can be positive or negative real ...
- 39
2
votes
1
answer
41
views
Modeling $-\ln(1 - w \cdot \sigma(x))$ as disciplined convex programming
Given $0 < w \leq 1$, I would like to use the function:
$$
-\ln(1 - w \sigma(t)),
$$
where $\sigma(t) = 1 / (1 + \exp(-t))$ is the sigmoid function, in my objective. It's a bit tedious, but this ...
- 131
2
votes
1
answer
313
views
Quadratic optimisation with $\ell_1$ constraints with CVXPY
Crossposted on Mathematics SE
I seek to minimize a convex quadratic objective subject to linear and $\ell_1$-based equality constraints. When I turn to CVXPY, an error is raised indicating that it ...
- 21
2
votes
1
answer
107
views
How to model these constraints correctly
$W$ is a vector of $N$ complex elements.
$D$ is a binary variable
The requirements are:
when $D==1$, $L_{\min}\le ||W||_2^2\le L_{\max}$
and when $D==0$, $||W||_2^2=0$
I have formulated the following ...
- 2,397
2
votes
0
answers
164
views
Global optimizers handling minimization of an expression arising from the likelihood of a multivariate normal
I am interested in converting the following optimisation problem into a form that an exponential cone and/or SDP solver such as MOSEK can handle. This is a multivariate version of the question I ...
- 269
2
votes
0
answers
74
views
Regularize for a bang-bang control
I have an optimal control problem with a state vector $\vec x$ and a control vector $\vec u\in[0,1]$.
If I were solving the problem without regularization I would write
$$
\min \lVert \vec x \rVert
$$
...
- 543
1
vote
1
answer
728
views
How to transform this problem with logarithmic objective function into an approximated convex optimization problem?
I have an objective function as follows
$\underset{x_{m,n}}{\max}\hspace{1mm}\hspace{1mm}\sum_{m=1}^{M}\log_2\left(\frac{\sum_{n=1}^{N}(1-x_{m,n})\omega_{m,n}+z}{\sum_{n=1}^{N}x_{m,n}\omega_{m,n}}\...
- 2,397
-2
votes
1
answer
200
views
How can I model this Hyperbolic constraint?
In this problem, $\beta_u$, $w_{u,c}$ (a vector of complex elements), $x_u$ are optimization variables.
Now,
$||2\sqrt{\frac{\pi_u}{2}}\beta_u; h_{u,c}^{\rm H}w_{u,c}-\frac{1}{2\pi_u}x_u-1||_2\le h_{u,...
- 2,397