# Tagged Questions

**3**

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### Why eigenvectors optimize this orthogonally constrained nonlinear minimization problem?

Given a $p \times p$ positive definite matrix $\Sigma$, why eigenvectors of $\Sigma$, stacked as columns of a matrix $R \equiv [r_1 \, r_2 \, \ldots \, r_p]$, optimize the following orthogonally ...

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**0**answers

99 views

### Modifying a QP to incorporate more constraints

Consider the following problem:
$$\min \sum_{i=1}^n (Y_i - Z^{(i)})^2 \\
\text{subjected to}~ \epsilon_k^{\top}(X_j-X_k) \leq Z^{(j)}-Z^{(k)} ~ \forall k,j = 1 \ldots n. $$
where $\epsilon_1, ...

**3**

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**1**answer

181 views

### Intuition on a certain class of quadratic optimization problems

Let $\mathcal{X} = \{\mathbf{X}\in\mathbb{C}^{d\times d}:\|\mathbf{X}\|\leq 1\}$, where $\|\cdot\|$ is the Frobenius norm. Let $\mathbf{y}\in\mathbb{C}^{d\times 1}$. We are familiar with the following ...

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64 views

### Optimization with differential inequality constraint

Consider the closed set $[t_1,t_2]⊂R_{>0}$ and $V(t):[t1,t2]→R_{>0}$ being a continuous and piecewise continuously differentiable function. We want to find a continuously differentiable function ...

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**0**answers

122 views

### Quadratic optimization with parameter in constraint

Disclaimer: I posted the same question on math.stackexchange. However, the FAQ suggests to post research-level questions in this forum.
Question: Given a function $q: \mathbb R^{N\times N}\mapsto ...

**5**

votes

**1**answer

280 views

### Solve equation with matrix variable

I want to solve a matrix $\Omega$ from a equation $\sum_k (\Omega + \Theta_k)^{-1} = Q$. The $Q$ and $\Theta, \forall k=1...K$ are known, and are positive definite matrices. $\Omega$ also has to be ...

**5**

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230 views

### Simultaneous maximization of two Generalized Rayleigh Ritz Ratios

Consider hermitian positive semi-definite matrices $A_1$ and $A_2$. Consider also positive definite matrices $B_1$ and $B_2$. I want to maximize the minimum of the two Generalized Rayleigh Ritz ratios ...