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.

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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 - \...
Dan Berkenstock's user avatar
8 votes
1 answer
315 views

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 ...
David's user avatar
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8 votes
1 answer
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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}\...
KGM's user avatar
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8 votes
1 answer
279 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 $\...
Apprentice's user avatar
6 votes
0 answers
436 views

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 ...
Dupin's user avatar
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5 votes
1 answer
227 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 ...
Brannon's user avatar
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5 votes
2 answers
167 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 $...
cfp's user avatar
  • 259
5 votes
1 answer
444 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: ...
Hussein Sharadga's user avatar
4 votes
1 answer
214 views

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 ...
Lukas Dauterman's user avatar
4 votes
1 answer
159 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 ...
LowOdds's user avatar
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0 answers
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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: $$ \small\min_{A,B,C} \| Y_A - AX_A \|_F + \| Y_B - BX_B \|_F + \| Y_C - CX_C \|_F + \lambda_1 \|B - A^2\|_F + \lambda_2 \|C - A^4\|_F $$ ...
ARandomName's user avatar
3 votes
1 answer
313 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 $[a, 1, b] \in \text{ExpCone}$. ...
worldsmithhelper's user avatar
3 votes
2 answers
240 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 ...
dourouc05's user avatar
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3 votes
1 answer
395 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 ...
Sasin's user avatar
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3 votes
1 answer
337 views

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}-...
KGM's user avatar
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3 votes
2 answers
125 views

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 ...
KGM's user avatar
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2 votes
1 answer
223 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 ...
jam123's user avatar
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2 votes
1 answer
90 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 ...
KGM's user avatar
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2 votes
1 answer
148 views

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. ...
Aidan Donnelly's user avatar
2 votes
0 answers
155 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 ...
cfp's user avatar
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2 votes
0 answers
75 views

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 ...
Allen Zhang's user avatar
2 votes
0 answers
69 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 $$ \min \lVert \vec x \rVert $$ ...
Richard's user avatar
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2 votes
1 answer
387 views

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 ...
jbuddy_13's user avatar
  • 519
1 vote
1 answer
640 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}}\...
KGM's user avatar
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1 vote
1 answer
96 views

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. $...
Muhammad's user avatar
1 vote
0 answers
42 views

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 ...
user760900's user avatar
-1 votes
0 answers
22 views

how to implement the correlation coefficient in cvxpy and how to rewrite cp.diff(cp.cumsum(x)/(cp.cumsum(x)[-1])

suppose that I have 2 sets of data, x and y,where x can be ...
Allen Zhang's user avatar
-2 votes
1 answer
186 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,...
KGM's user avatar
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