Questions tagged [disciplined-convex-programming]
Disciplined convex programming (DCP) is a system for constructing mathematical expressions with known curvature from a given library of base functions.
29 questions
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Penalize absolute value while keeping the problem DPP (CVXPY)
I am trying to implement the objective function max a . x + c . abs(x - g). where all elements of c are non-positive, ...
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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 ...
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Convex approximation of a constraint
I have a constraint given as
$
\left|x_n+\beta x_{n+ 1}\right|-\varepsilon_{ky}\left|x_{n}\right|\leq0\hspace{1em}\forall n=1,2...,N
$ I need to convert this into a convex form to implement in CVX. $...
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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 ...
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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 $...
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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 ...
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Handling Variable Division in CVXPY for Calculating Annualized Rate of Change
I am working with a dataset that contains multiple entries for different IDs across various years. Some IDs might have a gap of years between entries. My goal is to solve an optimization problem using ...
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How to rewrite a constraint with sum of convex and concave components to satisfy DCP rule?
suppose that decision variable is X with N dimensions, and one type of the constraint is ...
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How to linearize or fix this disciplined convex programming error?
How can I linearize this constraint
$$d_{u,c}\sigma \le \|{\bf f}_{u,c}\|^2\le Td_{u,c}$$
$\sigma$ is a very small number based on scale of $f$
$T>0$, ${\bf f}_{u,c}$ is optimization variable, a ...
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MIQP — CVXPY unable to treat summation of variables as a variable
I have a quadratic integer programming assignment problem. The goal is to assign riders seats on a bus such that distance between any two riders is maximized; however, the importance of each objective ...
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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:
...
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3
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1
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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 $[a, 1, b] \in \text{ExpCone}$.
...
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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 ...
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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 $\...
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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 ...
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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
$$
\min \lVert \vec x \rVert
$$
...
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4
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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
2
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1
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Constraint raises DCP Error
I have defined a problem which will minimize the cost of to run a pump. That is defined as the objective of the problem.
...
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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}}\...
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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,...
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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 ...
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351
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How can I convexify (allowed some approximation) the objective function?
I have a known matrix, $H$ of size $U\times B$.
The optimization variable is $D$ of same size, which is binary
Now I have $$S_u=\frac{\sum\limits_{b=1}^{B} D_{u,b}H_{u,b}}{\sum\limits_{b=1}^{B}H_{u,b}-...
- 2,397
4
votes
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Make Optimization term fit into DCP rules
I want to make a term in an objective function I am working with fit into DCP for CVXPY.
I am working on replicating this research paper for an active learning problem. Specifically equations 5 is ...
3
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2
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270
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DCP representation of a convex quotient of affine functions
I am trying to represent the following inequality:
$$\frac{x}{1-x} \leq y \qquad\mathrm{with}\qquad 0<x<1$$
The function on the left is convex (its second derivative is always positive over ...
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Help with constrained or regularized optimization problem involving variable matrices and powers of matrices (or perhaps matrix logarithms)
I am attempting to solve the following optimization problem:
$$
\small\min_{A,B,C} \| Y_A - AX_A \|_F + \| Y_B - BX_B \|_F + \| Y_C - CX_C \|_F + \lambda_1 \|B - A^2\|_F + \lambda_2 \|C - A^4\|_F
$$
...
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Disciplined convex programming representation of $x\sqrt{1-x}$
Anyone have an idea for a disciplined convex programming (DCP) representation of the concave function $x\sqrt{1-x}$, which is defined over the domain $[0,1]$?
The Taylor series about $x=0$ is $$x - \...
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How to make constraints satisfy disciplined convex programming guidelines?
How do I turn my convex constraints (described below) into constraints that are DCP so that I can solve them in CVXPy? Is there some ``cheat sheet'' of standard tricks?
I'm trying to implement the ...
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8
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How to resolve this issue in multi-objective optimization?
I have the following multiobjective optimization problem. The objectives are non-conflicting.
The Optimization Problem:
$$\underset{\large{a^{(l)}_{c,u},f^{(l)}_{c,u},z_{l,t},l\in\mathcal{L}}}{\max}\...
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Disciplined convex programming representation of $x\cdot\min x$
How can I reformat the problem below to follow DCP rules?
DCP rules are Disciplined Convex Programming Rules that allow convex programs to be solved. DCP
Is there a way to reformat the problem ...
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