Questions tagged [disciplined-convex-programming]

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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}}\...
-2
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1answer
63 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
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1answer
67 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
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1answer
242 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}-...
4
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1answer
81 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 ...
3
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2answers
131 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 ...
4
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0answers
42 views

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: $$ \small\min_{A,B,C} \| Y_A - AX_A \|_F + \| Y_B - BX_B \|_F + \| Y_C - CX_C \|_F + \lambda_1 \|B - A^2\|_F + \lambda_2 \|C - A^4\|_F $$ ...
8
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4answers
348 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 - \...
6
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0answers
242 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 ...
8
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1answer
305 views

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}\...
8
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1answer
258 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 ...