Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 46290

Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.

26 votes
1 answer
1k views

Finding the closest matrix to $\text{SO}_n$ with a given determinant

$\newcommand{\GLp}{\operatorname{GL}_n^+}$ $\newcommand{\SLs}{\operatorname{SL}^s}$ $\newcommand{\dist}{\operatorname{dist}}$ $\newcommand{\Sig}{\Sigma}$ $\newcommand{\id}{\text{Id}}$ $\newcommand{\SO …
Asaf Shachar's user avatar
  • 6,741
11 votes
1 answer
564 views

Is there a "formula" for the point in $\text{SO}(n)$ which is closest to a given matrix?

$\newcommand{\Sig}{\Sigma}$ $\newcommand{\dist}{\operatorname{dist}}$ $\newcommand{\distSO}[1]{\dist(#1,\SO)}$ $\newcommand{\distO}[1]{\text{dist}(#1,\On)}$ $\newcommand{\tildistSO}[1]{\operatorname{d …
Asaf Shachar's user avatar
  • 6,741
3 votes
1 answer
261 views

When is the optimum of an optimization problem affine in the constraint parameter?

While working on a variational problem I have reached to the following question: Let $f:(0,\infty) \to [0,\infty)$ be a $C^1$ function satisfying $f(1)=0$. Suppose that $f(x)$ is strictly increasing …
Asaf Shachar's user avatar
  • 6,741
3 votes
0 answers
108 views

Are square configurations the only critical points of the energy on the circle?

$\newcommand{\S}{\mathbb{S}^1}$ $\newcommand{\la}{\lambda}$Let$$M=\{(x_1,x_2,x_3,x_4) \in (\S)^4\,\, |\,\, \text{ all the } x_i \, \text{ are distinct}\} $$ Define $E:M \to \mathbb{R}$ by $$E(x_1,x_2 …
Asaf Shachar's user avatar
  • 6,741
3 votes
1 answer
133 views

Is the smallest root of this quartic always the closest point on the Hyperbola? [closed]

Let $a>b>0$. Suppose we want to minimize $$ f(x)=(x-a)^2+(1/x-b)^2, $$ over $x>0$. Equating $f'(x)=0$ leads to the quartic equation $$ g(x)=x^4-ax^3+bx-1=0. \tag{1} $$ Question: Is the smallest positi …
Asaf Shachar's user avatar
  • 6,741
2 votes
1 answer
154 views

Is the optimum of this problem convex in the constraint parameter?

Let $f:\mathbb R^+ \to \mathbb R$ be a smooth function, satisfying $f(1)=0$, and suppose that $|f|$ grows with the distance from $1$: $|f(x)|$ is strictly increasing when $x \ge 1$, and strictly dec …
Asaf Shachar's user avatar
  • 6,741
1 vote
1 answer
190 views

Is the minimum of a constraint optimization problem differentiable in the constraint parameter?

Let $h:\mathbb R^{>0}\to \mathbb R^{\ge 0}$ be a smooth function, satisfying $h(1)=0$, and suppose that $h(x)$ is strictly increasing on $[1,\infty)$, and strictly decreasing on $(0,1]$. Let $s>0$ b …
Asaf Shachar's user avatar
  • 6,741