Tagged Questions
0
votes
1answer
33 views
How to re-parametrize for quadratic minimization?
Given a real-rectangular matrix $S$ and inorder to solve this simple quadratic programming problem:
Minimize $w'S'Sw = \|S w\|^2$ over $w$ subject to
$e^Tw = 1$ and $w \geq 0$
using a solver I ...
0
votes
0answers
100 views
Optimization problem given a known solution space
Here is my problem.
I have to find four points in 3D (x1,y1,z1; x2,y2,z2; x3,y3,z3; x4,y4,z4) that satisfy some given quadratic constraints. In addition, I have a solution space in the form of a set ...
0
votes
1answer
89 views
Convex optimization problem to quadratic programming problem
Briefly, have the following problem:
\begin{equation}
\sum_{i = 0}^n a_i \ (max [ F_i( \bar x ), 0 ] )^2 \rightarrow min, \\\\
s.t.\\\\
A \bar x \leq b
\end{equation}
where $ F( \bar x ) $ is a ...
4
votes
2answers
149 views
Analog of Simplex Method for Quadratic Programming
It happened so I need to work with an algorithm for solving QP problems. The main issue here is that I can't find any references to this algorithms (at least no references in sources in english). ...
0
votes
1answer
46 views
Feasibility of a given set of Quadratic Forms
This arises as a part of my work. Given a positive number $t$, two hermitian matrices $P_1$ and $P_2$, I am interested in knowing if a unit norm vector $z$ exists such that
\begin{align}
...
0
votes
2answers
66 views
Optimize quadratic problem under collinearity boundary condition
Summary
Given the optimization problem
$$
\min_{d\in\mathbb{R}^{n\times 2}} \text{trace}\big( d^T Q d+Cd\big)
$$
for some $n\times n$-matrix $Q$ and another matrix $C\in\mathbb{R}^{2\times n}$, I'd ...
2
votes
1answer
303 views
How to convert quadratic programming problem to matrix form
I am new to this topic and am looking at an example I can't figure out. Can someone please help explain how this example creates the matrices used in the solver? Thanks!
This is the PROBLEM
...
1
vote
1answer
168 views
Linear least squares with non-negativity constraint
I am interested in the linear least squares problem:
$$\min_x \|Ax-b\|^2$$
Without constraint, the problem can be directly solved. With an additional linear equality constraint, the problem can be ...
2
votes
2answers
123 views
Finding the closest vector subject to an absolute constraint
I'm trying to solve the following problem:
$$\min_b \|d-b\| \\
\text{s.t. } |Ab|^2 \leq y
$$
or equivalently
$$\min_b \|d-b\| \\
\text{s.t. } |Ab| \leq c = \sqrt{y}
$$
Both $d$ and $b$ are vectors. I ...
2
votes
0answers
61 views
Software to optimize a quadratic program with quadratic constraints
I'm working in eight dimensions and want to minimize $x^TAx$ under the constraints $x^TBx \geq c$. Unfortunately, A is not positive semidefinite. Worse, I am almost positive that my domain is not ...
0
votes
2answers
315 views
How to solve this quadratically constrained quadratic programming problem?
Could you please shed some lights on this? (Not a homework problem)
I am looking for solutions to solve the following problem:
$$\text{max } || X b || \text{ s.t. } || b - b_0 || < a, || b || = ...
1
vote
1answer
982 views
Matlab Trust-region-reflective algorithm warning
I am very new to matlab and trying to solve portfolio optimization problem (minimizing the variance) using quadprog:
...
