0
votes
0answers
22 views

Fitting noise with Levenberg–Marquardt algorithm

I've got a sample of noise from a microphone, and I'm trying to fit a curve to the data using the Levenberg–Marquardt algorithm. However, I can't seem to find a good starting function. I've tried a ...
3
votes
1answer
67 views

Does having a zero eigenvalue preclude a matrix from being indefinite?

If a $3\times3$ matrix has a positive eigenvalue, a negative eigenvalue, and a zero eigenvalue, is it then, by definition, indefinite? I think so, since the matrix has both a positive and a negative ...
1
vote
1answer
186 views

Definition of tangent cone in continuous optimization .

Looking at the definition of tangent cone in continuous optimization : If $M$ is a open subset of $\mathbb R^n$ $x \in M$, The tangent cone of $M$ at $x$ is defined by $$\mathbb T (M, x) = \big\{d ...
7
votes
1answer
163 views

$\max\min$ problem

Suppose there is a real valued function $f(x,y)$ where $x,y$ are vector variables $x\in\mathbb{R}^n$ $y\in\mathbb{R}^m$. Moreover $f$ is strictly/concave in $x$ and strictly/convex in $y$. $f$ is also ...
0
votes
1answer
480 views

Max function is continuous and concave-convex?

Let $A \subset \mathbb{R}^n$ and $M \subset \mathbb{R}^{n \times m}$ be discrete sets of cardinality $N \geq 1$. Consider the function $f: \mathbb{R}^n \times \mathbb{R}^m \rightarrow \mathbb{R}$ ...
2
votes
1answer
455 views

When $\min \max = \max \min$?

Let $X \subset \mathbb{R}^n$ and $Y \subset \mathbb{R}^m$ be compact sets. Consider a continuous function $f : X \times Y \rightarrow \mathbb{R}$. Say under which condition we have $$ \min_{x \in ...
0
votes
1answer
186 views

Maximize function of two variables

Let $f: X \times Y \rightarrow \mathbb{R}$ be a continuous function, where $X \subset \mathbb{R}^n$ and $Y \subset \mathbb{R}^m$ are compact sets. Say under which conditions we have that $$ \max_{x ...
1
vote
0answers
45 views

equivalence between primitive and dual

I have a problem about the duality gap of the primitive problem and the dual problem. This problem comes from a probabilistic model named Lagrangian UVM. As this figure shows, this is a trinomial ...
0
votes
1answer
266 views

Generating a random monotonically increasing polynomial?

Given a polynomial $y : \mathbb{R} \mapsto \mathbb{R}$ of degree $p$: $$ y(x) = \sum_{k=0}^p c_k\, x^k,$$ can a random set of coefficients $\{c_0, \cdots ,c_p\}$ be generated such that $y$ is ...
3
votes
2answers
427 views

A naive approach for nonlinear optimization on several real variables and one natural variable. Give examples of (potential) failure

Motivation: Example. To solve a problem on evaluating the maximum of a product of $n$ real variables subject to an equality constraint on its sum $S$ ($=100$), I used the Lagrange multipliers method ...