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.

76 questions
Filter by
Sorted by
Tagged with
49 views

### Linear Programming with bounds on magnitude

I have a set of halfplanes $H$, and a target vector $T$. My goal is to find the vector $v$ closest (2-norm) to vector $T$, such that $v$ is in the intersection of all of the halfplanes. This can be ...
1 vote
64 views

### 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 ...
150 views

299 views

### 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 ...
181 views

### 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?
273 views

### 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 ...
1 vote
88 views

### 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 ...
47 views

### 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 ...
352 views

### 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 ...
1 vote
53 views

### 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 ...
104 views

### Generally quadratic convex problem with one non-convex term

How would you approach a standard convex quadratic problem with convex constraints but one non-convex term ? Say $|x|^{0.4}$. $$\min_x \frac{1}{2} x^{T}Qx + g^Tx + c^T \mathrm{sign}(x) |x|^{0.4}$$ ...
195 views

285 views

### Which optimization method can be used to do the following?

I've the following system of equations for studying information flow in the below graph, $$\frac{d \phi}{dt} = -M^TDM\phi + \text{noise effects} \hspace{1cm} (1)$$ Here, M is the incidence ...
139 views

The quadratic knapsack problem (QKP) $$\max_x x^TPx$$ $$\mathrm{s.t.}\;\;w^Tx\leq c,\; x\in\{0,1\}$$ where $P\geq0, w\geq0$ elementwise, is well studied and has existing solvers. My problem below ...
1 vote
6k views

### Why am I getting this DCPError?

I'm trying to optimize a binary portfolio vector to be greater than a benchmark using CVXPY. ...
144 views

158 views

### Multi-matrix orthogonal basis problem

Suppose we are given a set of symmetric, positive definite matrices $A_1,A_2,\ldots,A_k\in\mathbb{R}^{n\times n}$. Is there any numerical method or reduction to a known problem (e.g. eigenvalue ...
120 views

### Approximating solutions to quadratic recurrence boundary value problem

Cross-posted from Math Stackexchange: https://math.stackexchange.com/questions/2421964/approximating-solutions-to-quadratic-recurrence I have a branching process problem that has been reduced to ...
1 vote
134 views

I have a quadratic binary optimization problem of the form \begin{align} &\max x^TQx \cr &\text{subject to }x\in\mathcal{X}\subseteq\{0,1\}^n, \end{align} where $\mathcal{X}$ is the feasible ...
1 vote
165 views

1 vote
601 views

### What is the fastest method for solving a quadratic programm repeatedly,( warmstarted)?

I would like to solve the following optimization problem \begin{align} \min_{x\in [0,1]^n} x^T p+ \frac{1}{2\lambda} x^T Q x \end{align} $Q$ is a positive semidefinite matrix. $\lambda>0$ is a ...
1 vote
58 views

I am looking at a real-world resource allocation problem that is cast as a quadratically-constrained linear program of the form $$\max\langle f,x\rangle$$ subject to \begin{aligned} m \leq\,\, &... 1 vote 1 answer 156 views ### How to efficently solve: min \sum_{ij}(a_{ij}x_{ij}^2 + b_{ij}x_{ij}) s.t I am trying to solve the following problem, where a_{ij} \ge 0 \ \forall i,j: \begin{align} \mbox{minimize}\quad & \sum_{i=1}^m\sum_{j=1}^n (a_{ij}x_{ij}^2 + b_{ij}x_{ij})\\ \mbox{subject to}\... 1 vote 1 answer 213 views ### Reformulation of optimization problem I am looking for some helps concerning an optimization problem. I have an optimization problem defined on two sets \mathcal{X}=\{x_i\}_{i=1}^n  and \mathcal{Y}=\{y_j\}_{j=1}^m  and described as ... 6 votes 1 answer 1k views ### Algorithm for solving system of quadratic equations and linear equations Let x \in R^N. From a Spectral Chebyshev collocation method, I have a system of quadratic and linear equations. Denote them, x^T Q_i x + L_i^T x = 0 $$and$$ A x = 0 $$Furthermore, I know ... 4 votes 0 answers 174 views ### Eigenvalue-style optimization with quadratic constraints Suppose A\in\mathbb{R}^{n\times n} is symmetric and positive definite and that we have several symmetric matrices B_i\in\mathbb{R}^{n\times n} that are low-rank and indefinite. I need an ... 5 votes 2 answers 4k views ### How to determine whether two cylinders intersect or not? Considering any two cylinders, defined as: the center of their bottoms A_i, the radius of their bottom R_i, the unit vector W_i of their axis direction, and the length L_i of the cylinders, ... 1 vote 1 answer 602 views ### How to formulate variance minimization as a mixed integer quadratic program I have a mixed integer quadratic problem and my objective function is as follows$$\arg \min \operatorname{Var}(f(x),g(x)) + \operatorname{Var}(c(x),d(x)) + \cdots$$where f, g, c d are ... 0 votes 1 answer 97 views ### Can Variance be replaced by absolute value in this optimization problem Initially I modeled my objective function as$$\arg \min \operatorname{Var}(f(x),g(x)) + \operatorname{Var}(c(x),d(x)) + \cdots$$where f, g, c, x are linear functions. To be able to solve ... 6 votes 1 answer 6k views ### Convex Optimization problem with sum of absolute value constraints How to solve the optimization problem written below?$$\begin{align} &\operatorname{argmax}\limits_{a}\; a^T b - \frac{1}{2} a^T X a\\ &\text{subject to } \sum_i |a_i|=4,\; \sum_i a_i = 0 \...
Can you advise me any kind of existing software that can help to solve the disjunctive programming problem? The problem is the following. We have unit 3D planes $\Pi_{1}, \ldots, \Pi_{N}$ (they are ...
### Solve $AX = B$ where $X^T X = C$
Is there a natural way to find the solution to $$AX = B, X^TX = C \enspace \text{?}$$ $X$ is a matrix and has a small number of rows, and $A$ is sparse. An approximate solution would be fine.