Questions tagged [quadratic-programming]

Question 1

I have a constraint optimization problem where the Objectif function is the sum of quadratic functions of the form $$ C_i = a_i g_{i}^2 + b_i g_{i} + c_i $$ $\{g_i\}$ are the variables, $\{a_i\},\{b_i\...

Question 2

Let $R$ be some rectangle: $R=[a_1,b_1)\times \dots\times [a_n,b_n)\subset \mathbb{R}^n.$ Suppose $C$ is some $n\times n$ real positive-definite matrix. Is there a closed form for the min and max of $...

Question 3

Context and setup I am developing a library for multi-objective optimization. The idea is that instead of doing gradient descent, we have a Jacobian matrix whose rows are the gradients of our ...

Question 4

I appologise in advance if this is a simple question. I have been trying to check some references like Boyd's book, but i can't piece together the parts that I need to asnwer this question. I've tried ...

Question 5

I'm writing to ask for your advice on an optimisation problem (unfortunately I'm not an expert), namely: \begin{array}{ll} \min\limits_{x \in \mathbb{R}^n} & \frac{1}{2} \| \mathbf{x} - \mathbf{y}...

Question 6

In introducucing the support vector machines we have that we have $N$ vectors of dimension $p,$ $\{\textbf{x}_i\}_{i=1}^N$, we also have $\{y_i\}_{i=1}^N$ where $y_i\in\{-1,1\}$. If the two groups are ...

Question 7

Consider the following constrained quadratic optimization problem: $\min_{\mathbf{u}} \quad \mathbf{u}^T \mathbf{H} \mathbf{u} + \mathbf{u}^T \mathbf{g}$ subject to: $\mathbf{u}_{\text{min}} \leq \...

Question 8

I'am having problems understanding the a step in the solution proposed by my teacher(s) for the problem to minimize $\frac{1}{2}(x-\bar{x})^\top Q(x-\bar{x}) + c^\top(x-\bar{x})$ subject to $Ax = b$, ...

Question 9

I currently have the following problem to solve : $$ \underset{\mathbf{x}\geq \mathbf{1}}{\min} \quad \mathbf{x}^T\mathbf{Q}\mathbf{x}. $$ Here $\mathbf{x} \geq \mathbf{1}$ refers to elementwise ...

Question 10

I am trying to dualize a QP where the quadratic term is in the objective and the constraints are linear where Q is symmetric positive definite. $$ \begin{align*} \min \quad & \frac{1}{2} x^T Q x + ...

Question 11

Problem Formulation We aim to solve the following convex quadratic optimization problem: Objective Function: Minimize: $$ f(x) = \frac{1}{2} x^\top Q x + q^\top x, $$ where: ( Q ) is a positive ...

Question 12

I have a set of quadratic costs, where cost $i$ is of the form $$ f_i(x) = \frac{1}{2} x^T Q_i x + b_ix$$ which means the gradient is $$ \frac{df}{dx}(x) = \sum_i Q_ix + b_i$$. When optimizing these ...

Question 13

I want to find the biggest ellipsoid of fixed axes contained within a given box. More precisely, assume I want to maximize the Mahalanobis distance $(x-\mu)^T \Sigma^{-1} (x-\mu)$ where $\mu$ and $\...

Question 14

Let $X,Y\in \mathbb{R}^{d\times n}$ and $W\in\mathbb{R}^{d\times d}$. Is there a closed-form solution to the following minimization problem? $$\min_W \|WX - Y\|_F^2, \quad W \succeq 0.$$

Question 15

I'd like to minimize the trace of $P - XHP - PH^T X^T + XSX^T$ with the constraints that every entry of $X \geq 0$ here $P$ is $n$ by $n$ positive definite, $H$ is $m$ by $n$, S is $m$ by $m$ positive ...

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Questions tagged [quadratic-programming]

How to model fixed costs that activate only when a quadratic variable is nonzero?

Min and max of a quadratic in a rectangle

How does one differentiate the solution to a quadratic problem with respect to its parameters?

QP with additional inequality constraint. Is the solution the projection?

How to project point onto polyhedron?

Will the new optimisation problem give the old solution?

Cholesky decomposition of constrained quadratic program

Reformulation of a minimization problem concerning projection

Minimizing a pure quadratic function under box constraint

Clarifying different forms of the Dual of a quadratic Problem

Could you review my algorithm to assess its conceptual and practical validity for maintaining primal feasibility?

Compute hessian for a quadratic cost after nullspace projection

Find largest ellipsoid of given axes contained in a box

Closed-form solution to linear regression under positive semi-definite constraint

solving trace minimization problem in quadratic programming

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