# 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.

73 questions
Filter by
Sorted by
Tagged with
47 views

40 views

### Hyperbolic constraint as second-order cone

I have a problem which simplifies to: \begin{align} \max w &\\ w&\le xy \\ x,y&\le10 \\ x,y&\ge0 \end{align} Recognizing that $xy$ form a hyperbolic constraint, I can solve by ...
49 views

### Find a dual problem with one dual decision variable to the problem of finding the orthogonal projection of a given vector

Given the set $T_{\alpha}=\{x\in\mathbb{R}^n:\sum x_i=1,0\leq x_i\leq \alpha\}$ For which $\alpha$ the set is non-empty? Find a dual problem with one dual decision variable to the problem of finding ...
35 views

### Can I define constraints in Pyomo as a list?

I would like to define the following constraint in Pyomo $$W^\top{\bf 1}\le\hat w=\begin{bmatrix}\hat{w}_1&\hat{w}_2&\ldots&\hat{w}_N\end{bmatrix}^\top$$ where $W$ is a $2\times4$ matrix. ...
20 views

### Model definition in pyomo to solve online optimization problem

I am trying to model the attached online optmization problem in pyomo. Eventually, I am going to use the octeract solver to find the matrix soluions of W and G. I would like to ask advice about ...
65 views

76 views

### How to linearise this nonlinear constraint?

I have a constraint in the form $\sum_{n=1}^{N}x_{m,n}\omega_{m,n}\ge (t_u-1)\beta_u, \forall u, u=1,2,\cdots, U$ where $x_{m,n}$ is binary variable $t_u$ and $\beta_u$ are continuous optimization ...
136 views

### How to prove that the second-stage value function of a Stochastic Program is convex?

I am wondering to know how it is possible to prove that the second-stage value function in a two-stage stochastic program is convex on $x$ and $\xi$? A two-stage stochastic program can be defined as \...
35 views

### How to convert an element of a variable to a convex constraint using binary variables?

I defined a complex variable in cvx, but I want to restrict the first element of the variable to be larger than the max of the variable, but it doesn't work. Someone told me to transform it using a ...
20 views

### Correct way to define constraints in Pyomo

Can I know if the constraint below can be defined as follows in Pyomo for convex optimization. W and G are arrays of dimension M x N. ...
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,...