Questions tagged [quadratic-programming]
For questions about optimizing an objective function that is quadratic in its input variables. This could include questions about implementing solver methods or choosing the right solver for a given problem.
78 questions
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Upper and lower bounds on the worst case number of iterations of active set methods for quadratic programming
Fix some active set method of your choice (for the sake of clarity I spell out what I consider a vanilla active set method at the bottom of this post, but I'm interested in any variants you know about)...
- 809
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CVXPY - Convex difference of quadratic forms
I have a sparse optimization problem of the form:
$$\min_x c^T x + \| D x\|^2_2 + \| V x\|^2_2 - \| W x\|^2_2$$
$D$ is diagonal and $V$, $W$ are non-square matrices. I know that:
$$Q = D^2 + V V^T - ...
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2
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Can this problem be solved using convex optimization?
I have the following problem:
$$\begin{align}
\max & \quad \frac{\mu^\top x - c^\top|x - x_0|}{x^{\top}\Sigma x} \tag{1} \\
\text{subject to }
& \quad x \leq \mathbb{1} \tag{2}\\
& \quad ...
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Small quadratic programming problem - a simple Fortran code needed
I need to find a distance from a point in 3D space to a parallelepiped (a crystal lattice cell). The problem boils down to a quadratic programming task:
Let $L$ be a matrix of lattice vectors (row-...
- 143
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How to show that the solution of the following quadratic programming is non-negative
I have the following quadratic problem:
$max$ $a^Tx+0.5x^TAx$
$s.t: 1^Tx=1$
in which $a=[a_1, a_2,...,a_n]$ is a non-negative vector, and $1^T=[1,1, ..., 1]$. The hessian matrix $A$ has the ...
- 11
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1
answer
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Numerical Simulation of a Quadratic MIP with a highly rational term
I am interested in solving the following minimization problem:
$$
\begin{array}{cl}
\displaystyle\min_{x,y}&\displaystyle\frac{1}{K}\sum_{i=1}^{K}\left(\frac{x_{i}}{y_{i}}-\frac{X}{Y}\right)^{2} \\...
- 169
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Reuse linear mapping that provides the solution to least squares problem using LAPACK
LAPACK.gglse allows me to solve
min x^T Q x
s.t. A x = y
(in my present use case, $Q$ is symmetric positive definite)
without having to think about the numerical ...
- 809
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0
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55
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Reformulate a problem with concave objective function into a QP
I would like to convert this problem into a QP (Quadratic program).
$$\text{Maximize } \sum_{k=1}^{K}\sum_{n=1}^{N}log2(1+p_{kn}b_{kn})\\
\text{subject to } \sum_{k=1}^{K}\sum_{n=1}^{N}p_{kn}\leq P_{0}...
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How to ensure the numeric value is always positive in Optimization Python?
I am currently performing optimization onto a quadratic function by manually coding the algorithm:
$$\min f = x^T v x - r^T x\\
\text{subject to } x \geq 0\, .$$
Here, optimizing the function without ...
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278
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Absolute value constraint in quadratic programming optimization
$$
argmin(x,y)=x^2+y^2+2y
$$
$$
s.t.\ \ y=|x-10|
$$
How can I convert the absolute value constraint to the constraint matrix (GX<=h, AX=b) in cvxopt?
- 109
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1
answer
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Is solving QP easier than a QCQP with linear objective?
Is solving a $QP$ (i.e.: quadratic program, hence a quadratic objective function with linear constraints) easier than solving a $QCQP$ (ie.: quadratic constrained quadratic problem) with linear ...
- 141
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1
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Overconstraining in SQP
In Sequential Quadratic Programming we use an active set of the inequality constraints and handle them as equality constraints in the quadratic subproblem.
SQP is said to be able to deal with ...
- 111
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Implementation method selection for sparse constrained linear least squares or quadratic programming
I need to slove one optimization problem of quadratic programming. The number of optimization variables is about 16,000. The constraints include equality constraints and inequality constraints.
I have ...
- 213
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Can this simple quadratic optimization problem be turned into a simple eigenvalue problem?
I'm interested in a type of problem on this form
$$\min_{x} x^{T}Ax+x^{T}b \quad \text{s.t} \quad x^{T}x=1 $$
where $A$ is positive definite. As you can see, if it weren't for the $x^{T}b$ term in the ...
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Quadratic optimization with nonlinear vector term
I wish to minimize the quantity $$W=1/2x^TAx-x^Tg(y)$$ with respect to $x$ and $y$, which are vectors of unknowns. $A$ is a sparse square symmetric positive definite matrix and $g(y)$ is a vector with ...
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