# Questions tagged [quadratic-programming]

A quadratic program (QP) is an optimization problem in which the objective function is quadratic and the feasible region is a convex polytope.

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### Drawing a 3D object in a 3D environment, and converting to math [closed]

So I have been granted a free time and I want to work on a project but first I had to research. As we know, lines have infinite points, and with lines, we can create infinite shapes. I want to let ...
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### Complexity of Quadratic Programming where the symmetric matrix Q is positive semidefinite only in the feasible directions

playing around with stuff for my dissertation, I derived a quadratic problem in the general form \begin{equation} \begin{aligned} \min_{x} \quad & x^TQx + c^Tx \\ \textrm{s.t.} \quad & Ax \leq ...
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### Least squares problem with constrained solution [closed]

If $a_{m\times 1}$ and $Q_{m\times n}$ ($m<n$) are known, and we know every element of $b$ is between $[-1\ \ 1]$, how to determine $b$ to minimize $\|a+Qb\|_2$?
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### Quadratic Programming With Piecewise Linear Term

The problem I have can be defined as: $$\min \frac{1}{2}\mathbf{x}^T\mathbf{Q}\mathbf{x} + \mathbf{c}^T\mathbf{x}$$ s.t. linear equality constraints: $$\mathbf{Ax=b}$$ and linear inequality ...
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### Optimization question: maximize quadratic objective with semidefinite constraints

I recently encountered the following optimization problem: $\max \|AX\|_F^2$ subject to: $X\succeq0$ and $Xb_i\leq c_i$ for a collection of $T$ conditions: $i=1,\ldots,T$. Matrices $A$ and $X$ are ...
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### Solution of a linearly constrained quadratic programming problem [closed]

What is the solution of the following optimization problem: \begin{align} &\min{\mathbf{p}^\mathrm{T} \mathbf{B} \mathbf{p}}\\ &\text{subject to}: \mathbf{0}\leq{\mathbf{p}}\leq \mathbf{1}. \...
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### Efficiently factorize a KKT system with block diagonal upper corner

I have a system resulting from a quadratic energy minimization with linear equality constraints enforced with Lagrange multipliers which has the form: \begin{equation} A = \left[\begin{array}{c|c} \...
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### combinatorial and linear duality

Let $S$ be a finite set, and let $W$ be a nonempty set of subsets of $S$; we will identify every subset of $S$ with its characteristic function, a 0-1 vector in $\mathbb R^S$. The combinatorial dual \$\...
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### Block Covariance Matrix - Positive Definite? (Quadratic Optimization) [closed]

I have a covariance matrix C. I have then formulated an quadratic optimization problem that involves the following matrix in the quadratic form: [ C C ] [ C C ] However, the quadratic solver ...
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