Questions tagged [convex-optimization]
Convex minimization, a subfield of optimization, studies the problem of minimizing convex functions over convex sets. The convexity property can make optimization in some sense "easier" than the general case - for example, any local minimum must be a global minimum.
7
questions
12
votes
2answers
480 views
Convex Maximization with Linear Constraints
I am doing active research in convex maximization w.r.t. linear constraints. There are many cases which can be efficiently approximately solved, e.g., convex quadratic maximization, log-sum-exp ...
5
votes
1answer
249 views
Solving Quadratically Constrained Quadratic Program with Cross Product Terms Only
I'm totally new to the world of optimization and I have an optimization problem that I think it can be formulated as Mixed Integer Quadratically Constrained Quadratic Program (QCQP) but I'm not sure ...
4
votes
1answer
153 views
Cutting-planes application procedure for a specific problem
Sort of following up with this question. I reformulated another model to make it convex and possibly solve it with some cut generation method. I would like to double-check whether I am doing it ...
3
votes
1answer
138 views
Can we get the closed-form solution for this problem?
Can we get the closed-form solution for this problem?
\begin{align}
\min&\quad\sum_{i=1}^N\frac{K_i}{x_i\log_2(1+\frac{Q_i}{x_i})}\\
{\rm{s.t.}}&\quad\sum_{i=1}^N x_i\le X
\end{align}
wherein $...
3
votes
0answers
101 views
Existence of a transformation to convex optimization
Question
Does a transformation of the following problem to convex optimization exist?
\begin{aligned} \label{1}
\min_{\vec{x}, \vec{y}} \quad & F(\vec{x}, \vec{y}) \\
\textrm{s.t.} \quad
...
3
votes
2answers
214 views
How to make following constraint a convex one?
I would like to write a constraint as follows, where $x,y>0$ are optimization variables, and $a,b,c,d,A$ are positive constants. How to make it a convex constraint?
\begin{equation}
\frac{{ax}}{{\...
1
vote
1answer
104 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}}\...
