The quadratic-programming tag has no wiki summary.
4
votes
2answers
160 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). ...
4
votes
1answer
144 views
solution to $\min \|A-BXC \|$
I have the following problem. Let $A$, $B$ $C$ be real-valued matrices of size $m \times q$, $m \times n$, $p\times q$ respectively. I would like to find matrix $X$ of size $n\times p$ and maximum ...
3
votes
2answers
195 views
Quadratic equation to calculate a temperature from resistance
I'm trying to implement an electronic temperature sensor that gives a resistance value. The sensor is a Honeywell TD4.
In the datasheet, they give a table of values :
-40ºC => 1584Ω ±12Ω
-30ºC => ...
3
votes
2answers
91 views
A standard quadratic minimization problem
Consider the "Complex" Quadratic minimization problem
\begin{align}
\min_{\mathbb{x}\in \mathbb{C}^{N \times 1}}~\mathbf{{x}}^H\mathbf{Q}\mathbf{x}-2~\Re{(\mathbf{x}^H\mathbf{b})}+1
\end{align}
...
3
votes
1answer
126 views
How to use lagrange multipliers here?
I have a simple QP as below:
$\min L(x,y) = (x-5.1)^2+y^2$
such that
$(x-3)^2+y^2\geq1$
$(x-5.3)^2+y^2\geq1$
$(x-7)^2+y^2\geq1$
Intuitively, I think the optimal solution of the problem is ...
3
votes
1answer
151 views
Optimization problem with ratio objective
I need to solve the following optimization problem
$$
\text{maximize} \quad \frac{(a^T x)^2}{x^TBx+c^T|x|} \quad \text{subject to} \quad ||x||_1=1 \quad (\text{or alternatively} \quad c^T|x|=1),
$$
...
3
votes
1answer
578 views
what is the computational complexity of solving a quadratic program with linear inequality constraints
I'm aware of several solution methods and have several solvers at my disposal, but I can't for the life of me find analysis on the complexity. In particular, I'm interested in the complexity of ...
2
votes
1answer
51 views
Find my mistake: Solving quadratic programm by “brute force” triangularization
Do you know the feeling when you have proven something totally incredible? In fact, it is so incredible you do not believe it yourself. So you start looking for your mistake, for the one, small ...
2
votes
2answers
128 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
1answer
328 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
...
2
votes
1answer
58 views
Convex optimization and linear programming please help! :)
How would I write the following as a standard form LP? Minimizing $\sum_{i=1}^n x_i + c\max(a_i-x_i)$ for $a_i \ge 0$ and what is the optimal value for when $c=n$
How to express minimize $\frac{1}{2} ...
2
votes
0answers
62 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 ...
1
vote
4answers
92 views
Solution to a system of quadratics
I am learning about a Bell State, and am trying to show that they are entangled. I believe that the required proof is to show that the system
$$\alpha_0^2+\alpha_1^2=1$$
$$\beta_0^2+\beta_1^2=1$$
...
1
vote
1answer
404 views
Example of a quadratic programming problem with no optimal solution on vertices?
Is there a way to write a quadratic programming problem with
two variables
bounded, nonempty feasible region
linear constraints
and yet have none of the vertices of the region optimize the ...
1
vote
1answer
268 views
Markowitz portfolio optimization
Say that there are 5 assets with given mean values, standard deviations and correlations. Is it possible to find the expected return of a risk-seeking portfolio (maximum expected return) by using ...
1
vote
1answer
174 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 ...
1
vote
1answer
1k 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:
...
1
vote
0answers
43 views
Nearest point to a convex polytope
I am looking for fast, memory-efficient computational algorithms to solve the following problem:
Minimize: $||x - x*||_2^2$, subject to constraints $A x = a, B x <= b, l <= x <= u$,
where ...
1
vote
0answers
41 views
Minimize a complex quadratic subject to two convex quadratic constraints
I have the following the optimization problem
\begin{align}
\min_{\mathbb{x}\in \mathbb{C}^{N \times 1}}~&||\mathbb{x}^H\mathbb{u}||_2^2-2*Real\{ \mathbb{x^Hu}\}
\\\ ...
1
vote
0answers
58 views
Quadratic programming with simplex constraints
I have this quadratic function $x'Ax$ which is not convex. I want to maximize this function subject to the constraints that the solution x lies in a simplex such that $\sum_{i=1}^{n}x_i=1$. That means ...
1
vote
1answer
67 views
Issues with quadratic programming
I am trying to do a quadratic programming. I have an affinity matrix A, and I have to maximize certain function x'Ax. This is basically related to feature matching i.e matching points to labels
This ...
1
vote
0answers
73 views
Algorithm and solver for large, dense, positive-semidefinite integer QP
I am interested in the solutions of a very large quadratic programming (QP) problem
\begin{align}
\min_{x \in \mathbb{R}^n} & x^T Q x\\
\mathrm{subject\ to} & A x = b\\
& x \in \{0,1\}^n
...
0
votes
1answer
37 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
1answer
93 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 ...
0
votes
2answers
325 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:
$$\text{max } || X b || \text{ s.t. } || b - b_0 || < a, || b || = ...
0
votes
1answer
1k views
Using Matlab quadprog to solve markowitz model
I have the markowitz model shown below and I need to use the quadprog function to solve it (i.e get the values for w_i values). However I am a bit new to mat lab and not sure which definition of ...
0
votes
1answer
139 views
Find a best 4-tuple which fulfils a variable boolean formula
I am looking for an algorithm...
I have a kind of boolean formulae which contain $\wedge$, $\vee$, $+$ as arithmetic operator, relational operators ($<, >, \ldots)$, 4 integer constants $c_0, ...
0
votes
0answers
13 views
minimize absolute quadratic cost with quadratic equality constraint
I would like to optimize the following system:
$$\text{min}_q\, \sum_i^n |q^T M_i q| \text{ subject to }||q||=1$$
More details:
the size of the unknown vector $q$ is $4\times1$
$M_i$ is a matrix ...
0
votes
0answers
43 views
Solving for a sum of products
Following a question I asked yesterday, which yielded little success, I've refined my problem further to solving a system of equations.
In essence, I wish to solve for $h_n$ and $\hat{h}_n$ (for all ...
0
votes
0answers
29 views
Complexity of minimizing $ L_2$ norm subject to linear inequalities
What is the computational complexity of solving a quadratic program of the following form?
min $||x - c||_2^2$ subject to
$Ax \ge b$
[$x,c$ are $n\times 1$, $A$ is $ m \times n$, $b$ is $m ...
0
votes
0answers
102 views
Optimization problem given a known solution space
Here is my problem.
I have to find four points in 3D (x1,y1,z1; x2,y2,z2; x3,y3,z3; x4,y4,z4) that satisfy some given quadratic constraints. In addition, I have a solution space in the form of a set ...
0
votes
0answers
37 views
Is this a quadratic programming problem?
I have $N$ unknown 2D points ${\bf x} = (x,y)$ and I want to minimize:
$f({\bf x}) = \sum_{i=0}^{N-1}{(||x_{i+1} - x_i||_2 - c_i)^2}$
where c are $N-1$ known scalars. What is the simplest form that ...
0
votes
0answers
50 views
Solving non concave quadratic function in matlab with constraints
How can I solve non concave quadratic problem in matlab with constraints. I tried using quadprog but it doesn't work
0
votes
1answer
46 views
Feasibility of a given set of Quadratic Forms
This arises as a part of my work. Given a positive number $t$, two hermitian matrices $P_1$ and $P_2$, I am interested in knowing if a unit norm vector $z$ exists such that
\begin{align}
...
0
votes
2answers
68 views
Optimize quadratic problem under collinearity boundary condition
Summary
Given the optimization problem
$$
\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 ...
0
votes
1answer
52 views
Solving equation of the form $Axb^Tx = y$
I have a square, invertible $n\times n$ matrix $A$, and column vectors $b$ and $y$. I'd like to find a column vector $x$ such that $Axb^Tx=y$. I suspect there's some way to get it into a QP form, but ...
0
votes
0answers
39 views
A. Kaufman “Methods and Models of Operations Research”
There're 3 volumes (at least) of "Methods and Models of Operations Research" written by A. Kaufmann. So far I've found only first, called "Methods and Models of Operations Research", published in ...
0
votes
1answer
285 views
Are quadprog and portopt equivalent in Matlab?
What exactly is the difference between quadprog and portopt in Matlab? For example if I use quadprog (minimizing the variance) in a loop in which I continuously iterate through the expected returns of ...
