2
votes
3answers
225 views
Which method to apply to this problem?
I'm a programmer and I came a across an interesting problem. I'm sure there is a mathematical method or an algorithm to solve it, but I don't know where to start with the search no …
1
vote
2answers
81 views
Are Bregman divergences quasi-convex?
Given a convex set S ⊂ ℝd and an appropriately differentiable convex function f: S → ℝ, a Bregman divergence Bf(x, y) = f (x) - f (y) -〈x- y , ∇f (y …
1
vote
0answers
153 views
Optimization Game
I heard about a problem my friend had asked at my high school's math team, which was actually him just trying to figure out how to solve a game on his cell phone, but it is still i …
1
vote
1answer
138 views
Problem equivalent to “largest square in a cube”
The "largest square in a cube" problem, which asks for the largest square inside a cube, has a solution as can be seen on this page, which also says that the general problem in hig …
1
vote
2answers
132 views
Why is solving a MILP w/o an objective function so much faster?
When solving a MILP (mixed integer linear program) using a linear relaxation, the solver finds a feasible solution much faster if there is no objective function. The same problem w …
17
votes
2answers
716 views
Five Front Battle
Two generals are fighting a five front battle. Each general has 1 unit of army, which he divides into five separate armies that he sends to the five fronts. If one general sends mo …
2
votes
1answer
103 views
Algebraic characterization of transitive spaces of matrices
Fix an integer $d \ge 2$ and let $M_d$ be the space of real $d \times d$ matrices. Let $E$ be a vector subspace of $M_d$. We say that $E$ is transitive if $E \cdot \mathbb{R}^d_* …
3
votes
1answer
137 views
Maximizing Sparsity in l1 Minimization?
Consider the optimization problem
$$\min_x ||Ax||_1 + \lambda||x-b||^2,$$
where $A \in \mathbb{R}^{n \times n}$, $x,b \in \mathbb{R}^n$ and $\lambda$ is strictly greater than 0. …
0
votes
2answers
129 views
univariate prior corresponding to weighted sum of L1 and L2 penalties?
Is there a univariate probability distribution $p_{\lambda,\alpha}(\beta)$ over the reals, parameterized by $\lambda > 0$ and $1 >= \alpha >= 0$, such that $p_{\lambda,\alpha} \pro …
4
votes
3answers
131 views
Navigation solution for frictionless vehicles.
Looked around a bit and couldn't seem to find a similar question. (either that or it was worded with vocabulary above the multivariable calculus I've taken. :))
Roughly worded: I …
0
votes
1answer
126 views
Uniformly distribute a population in a given search space
I am trying to uniformly distribute a finite number of particles into a 2D search space to get me started with an optimization problem, but I am having a hard time doing it. I am t …
1
vote
0answers
56 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 glo …
0
votes
2answers
191 views
If a quadratic form is positive definite on a convex set, is it convex on that set?
Consider a real symmetric matrix $A\in\mathbb{R}^{n \times n}$. The associated quadratic form $x^T A x$ is a convex function on all of $\mathbb{R}^n$ iff $A$ is positive semidefin …
2
votes
1answer
100 views
Switching function for Bang-Bang nagivation
I'm attempting to develop an equation to determine the "switching time" for a control system. I've managed to work out a specific solution for when starting and ending velocities …
-1
votes
0answers
215 views
Closed form solution to linear program
Is it possible to obtain a closed form solution to a convex optimization problem? Specifically, the optimization function I am looking at is to maximize x over a convex polygon in …
