# Tagged Questions

**2**

votes

**2**answers

267 views

### Convex upper bound on a linear-fractional function

I have a function of the form $f(x,y) = \frac{x}{c+y}$ where $c$ is a positive constant, $c \ge x \ge 0$, and $y \ge 0$. I would like to find a convex upper-bound for this function. Is there a ...

**8**

votes

**1**answer

496 views

### Approximating a convex function by a piecewise linear function

Suppose I have a Lipschitz-continuous convex function $f:\mathbb{R}^n\rightarrow \mathbb{R}$. I wish to approximate it on the unit ball by a piecewise-linear function $g:\mathbb{R}^n\rightarrow ...

**10**

votes

**0**answers

361 views

### Functions approximated by rolling epicycle curves

Imagine a decreasing sequence of (positive) radii $r_1 > r_2 > r_3 > \cdots$
and a series of nested circles $C_1 \supset C_2 \supset C_3 \supset \cdots$
with these radii,
initially each ...

**2**

votes

**2**answers

738 views

### Interpolation Splines of Bounded Curvature

Given $n$ points $p_i=(x_i,y_i)$ on the [Euclidean] plane, and a positive real number $\rho$. Can we have a polynomial spline (e.g natural cubic spline) passing through all these points, such that: ...

**2**

votes

**1**answer

1k views

### Matrix approximation

Let A be an $m\times n$ matrix and $k$ be an integer. Assume that $A$ is non-negative. We want to find a scalar $\epsilon$ and an $n\times n$ matrix $B$ such that $A\leq A(\epsilon I + B)$ (where ...