The tag has no usage guidance.

learn more… | top users | synonyms

6
votes
0answers
557 views

Maximizing the matrix norm

Hi all, I wish to find a 3x3 rotation (orthogonal) matrix $\mathbf{R}$ such that it maximizes the following matrix norm: $||\mathbf{A} \mathbf{D}_r \mathbf{D}_b ||_2$ where $\mathbf{A}$ is a known $...
4
votes
1answer
2k views

Homogeneous system of polynomial equations

Hi all, Previously I asked a question that currently has no satisfactory answer Least sum squares given constraints on subcomponents It comes from an engineering problem. I was thinking to formulate ...
10
votes
2answers
2k views

Maximizing the Smallest Eigenvalue of a Diagonally Dominant Matrix

Assume that we have a full-rank diagonally dominant matrix $A$, all the diagonal elements of which are positive, all the non-diagonal elements are negative, and the sum of the absolute values of the ...
5
votes
1answer
2k views

Non-negative quadratic maximization

For a given symmetric and positive semidefinite $n \times n$ matrix $A$, we want to solve the problem $$\max_{||x|| = 1, \ x\geq 0} x^T A x.$$ Here, $x\geq 0$ indicates that $x$ must be component-wise ...
4
votes
2answers
2k views

Optimal knot placement for fitting piecewise-continuous linear functions to a nonlinear function

I encountered this problem in my research and it is turning out to be a surprisingly difficult one(for me, at least). Suppose we have a univariate nonlinear function $f(x)$ where $x \in [L,U]$. Our ...
6
votes
3answers
670 views

Some questions about Invexity

Recently, I am looking into a non-convex optimization problem whose points satisfying KKT conditions can be obtained. Then the problem becomes how to decide whether the KKT conditions are sufficient ...
2
votes
1answer
285 views

Can subgradient infer convexity?

It is known that If $f:U→ R$ is a real-valued convex function defined on a convex open set in the Euclidean space $R^n$, a vector v in that space is called a subgradient at a point $x_0$ in $U$ if for ...
0
votes
1answer
298 views

max length or size of a convex set

I want to maximize $||x-y||$ with $x$ and $y$ in $C$ where $C$ is the intersection of some discs. We assume the intersection is nonempty, and closed. I am thinking, how to formulate it as a ...
15
votes
1answer
2k views

A circle packing conjecture

Consider $n$ circles with variable radii $r_1,\ldots, r_n$ that pack inside a fixed circle of unit radius. In other words, all $n$ variable-radius circles are contained in the unit radius circle and ...
7
votes
5answers
1k views

Robust black box function minimization with extremely expensive cost function

There is an enormous amount of information about the common applied math problem of minimizing a function.. software packages, hundreds of books, research, etc. But I still have not found a good ...
31
votes
6answers
17k views

Is all non-convex optimization heuristic?

Convex Optimization is a mathematically rigorous and well-studied field. In linear programming a whole host of tractable methods give your global optimums in lightning fast times. Quadratic ...
1
vote
2answers
228 views

how to estimate a polyhedron(convex hull) classifier from data sample

Given a set of points $X\in\Re^D$, they have labels $Y\in${$-1,+1$}. I would like to separate the data labeled +1 and the data labeled -1 by a polyhedron. $min_w \sum_i \xi_i + \frac{1}{2}\|w\|_2^2$ ...
2
votes
0answers
161 views

modification of singlestart in global optimization

When minimizing a nonconvex function $f : \Omega \rightarrow \mathbb{R}$ that may have multiple minima, there are some very simple strategies to improve the odds of finding the global minimum point. ...