This is for questions on Quadratic Programming (QP). A QP problem is the problem of minimising or maximising a quadratic objective function subject to affine constraints.

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1answer
75 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 ...
0
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2answers
125 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
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1answer
953 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
720 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 ...
0
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1answer
63 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 ...
1
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1answer
728 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 ...
2
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2answers
202 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 ...
3
votes
2answers
248 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 => ...
2
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1answer
94 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 ...
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4answers
99 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 $$\alpha_0^2+\alpha_1^2=1$$ $$\beta_0^2+\beta_1^2=1$$ ...
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0answers
114 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 ...
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2answers
496 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 || = ...
3
votes
2answers
969 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 ...
0
votes
1answer
469 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 ...
1
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1answer
2k 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: ...
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2answers
2k 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 ...
1
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1answer
430 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 ...
4
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1answer
168 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 ...
0
votes
1answer
153 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, ...