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.

learn more… | top users | synonyms

0
votes
1answer
31 views

Linear programming with non-convex quadratic constraint

Could anyone let me know if the following linear programming problem can be solved in polynomial time or should be NP-hard? $\min c^Tx$ s.t. $x^TQx\geq C^2, x\in [0,1]^n,c\in ...
0
votes
1answer
27 views

Is a given point P outside a given bounding box, in Ax < b form

Given a point $x$ and a bounding box $B$ - let's say we have the unit normals $N_i$ of the sides (pointing inwards) and one point on each side $P_i$ - we can check if $x$ is inside $B$ as follows: ...
1
vote
1answer
38 views

Solving multiple $L_1$ penalties with quadratic programming

Starting from a simple $L_1$ penalization: \begin{equation} min_x \frac{1}{2}||y-x||^2_2 + \lambda||Dx||_1 \end{equation} We can solve this with quadratic programming via the dual problem: ...
0
votes
0answers
10 views

Basic quadratic programming - finding maximum for ellipsoid.

If I know that the maximum of my function of two variables can be found by the point on a linear constraint touched by the smallest ellipsoid...(look at picture for example, where the maximum is in at ...
-1
votes
0answers
12 views

quadratic programming with ellipse - why f' (x) = 0

Okay, so I've got my ellipse equation, and my constraints, and I want to find the optimum which in this case is the LAST point where my ellipse is within the constraint. My book tells me that I find ...
0
votes
0answers
30 views

Linear programming with quadratic constraints

I want to solve a problem of this form: $max_{y,k} \,\,\, w^\top y + C 1^\top k$ s.t. $k y^\top B^\top = I $ $A^\top y \geq b$ is there an algorithm that can solve such a problem? Is there an ...
0
votes
0answers
19 views

a question about relationship between KKT matrix equation and optimal solution of quadratic problem.

I have a question regarding how the KKT matrix plays in solving for optimization problem: Is it correct that the optimal solution for quadratic optimization problem with positive definite hessian ...
0
votes
0answers
28 views

Are box constraints problematic when using KKT conditions to solve quadratic programming problems?

I've dealt with quadratic programming before, but I've never seen something of this sort: $$\min \frac12 \|v\|^2 + \sum_ip_i$$ $$\text{s.t. }f(v,p)\ge0 $$ $$0\le p_i\le a$$ for some constant a ...
1
vote
0answers
74 views

Linear Programming with One Quadratic Equality Constraint

I have a problem which can be formulated as a Linear Programming with One Quadratic Equality Constraint: where variable x is n-dimensional vector and H is a Semi-Positive Definite n-by-n matrix. I ...
0
votes
0answers
13 views

Uniqueness of the solution to a quadratic opt problem

Consider a positive definite matrix $\boldsymbol H$, the known vectors ${\boldsymbol b}$ and ${\boldsymbol a}_i$. Now the minimization problem is casted with respect to the vector ${\boldsymbol x} $ ...
0
votes
0answers
24 views

Implementing SVM: Help converting equation into form of another

I'm currently programming a simple linear SVM (Support Vector Machine). For the optimization involved, I need to find a way to convert the equation $\sum\limits_{i=1}^L a_i ...
1
vote
2answers
30 views

Trace of quadratic function with 2 PSD matrices - convex?

If A & B are positive semi-definite, is this always convex: $$ trace(XAX^TB) $$ There was a similar question asked here: Trace of a quadratic function, Convexity and here: Confusion related to ...
0
votes
0answers
18 views

How to check if steepest gradient method will converge?

So I have this function $ f(x,y) = x^4 - 2x^2 +x + 4y^2 $ and I want to know if the steepest gradient method will converge if I pick an arbitrary point and apply said method. My initial thought ...
0
votes
1answer
36 views

How can I find the minimum and maximum?

Lets have the following equation: $f(x,y,y) = cos(x)^2+\frac{1}{1+x^3}+y^3+z$ I would like to find the minimum and maximum where $-2<x<2$ $-1<y<1$ $-2<z<1$ How can I do that, I ...
0
votes
0answers
25 views

Total unimodularity in quadratic programming.

I have a quadratic integer problem of the following form: \begin{align} minimize & \quad \tfrac{1}{2} x^T Q x + c^T x \\ subject \ to & \quad M x = 1 \\ & \quad x_i \in \{0, 1\} ...
0
votes
0answers
36 views

Finding an optimal set of weights for combining correlated classifiers

In order to combine classifiers that are correlated with one another, I would need to solve the following optimization problem: Find a vector $\mathbf{w}$ that minimizes $\mathbf{w}^T M \mathbf{w}$ ...
1
vote
0answers
41 views

Linear Complementarity Problem - multiple solutions, which one will it find?

If I have a inequality constrained system: w = Mz + q <= 0, z<=0, z^T w = 0 that for some given properties M and ...
0
votes
1answer
58 views

Minimization problem convex set

I'm trying to minimize the function: $$f(w)=w^T\mu+k\sqrt{w^T\Sigma w}$$ where $w$ is a vector in $W=\{x \in \mathbb{R}^n|x_1+...+x_n=1 , x_i \geq 0 \forall i\}$. The vector $\mu \in \mathbb{R}^n$, ...
0
votes
0answers
154 views

Minimum Curvature Path - implementation

I need to implement an algorithm which solves the Minimum Curvature Path problem. I found an interesting solution in this paper http://i.imgur.com/2EeGQKp.png. First, I decided to implement an ...
2
votes
1answer
111 views

Shortest Path and Minimum Curvature Path - implementation

Let's say we are given a race track, which may be described as a closed curve of given width (it may differ along the curve). My task is to implement an algorithm which finds two kinds of trajectories ...
2
votes
0answers
54 views

Quadratic Integer Programming

Would anyone mind helping me solve this problem $$ \min\space f(x) = \frac12 x^\mathrm TQx + bx + c \qquad \text{s.t. } \sum_i x_i=\lambda $$ where $x$ is a vector whose entries are positive ...
0
votes
0answers
20 views

Question concerning quadratic programming

Consider a quadratic program where you are given a polyhedron Ax <= b And you are given an arbitrary point F such that you want to maximize the distance from this point and you are guaranteed the ...
3
votes
2answers
75 views

$ k x^2 +4x = n $, Algorithm or any other method needed

I want to find any $n < 10^{18} $ so that the equation below has at least two pairs of solutions $(k, x)$ $ k x^2 +4 x = n $ constraints: $x > 10^6; \; x > k ; \; k, x \in \mathbb{N}$ I ...
0
votes
0answers
63 views

minimize absolute quadratic cost with quadratic equality constraint

I would like to optimize the following system: $$\text{min}_q\, \sum_i^n |q^T M_i q| \text{ subject to }||q||=1$$ More details: the size of the unknown vector $q$ is $4\times1$ $M_i$ is a matrix ...
0
votes
0answers
52 views

Solving for a sum of products

Following a question I asked yesterday, which yielded little success, I've refined my problem further to solving a system of equations. In essence, I wish to solve for $h_n$ and $\hat{h}_n$ (for all ...
0
votes
1answer
53 views

How to re-parametrize for quadratic minimization?

Given a real-rectangular matrix $S$ and inorder to solve this simple quadratic programming problem: Minimize $w'S'Sw = \|S w\|^2$ over $w$ subject to $e^Tw = 1$ and $w \geq 0$ using a solver I ...
0
votes
0answers
121 views

Optimization problem given a known solution space

Here is my problem. I have to find four points in 3D (x1,y1,z1; x2,y2,z2; x3,y3,z3; x4,y4,z4) that satisfy some given quadratic constraints. In addition, I have a solution space in the form of a set ...
1
vote
0answers
61 views

Nearest point to a convex polytope

I am looking for fast, memory-efficient computational algorithms to solve the following problem: Minimize: $||x - x*||_2^2$, subject to constraints $A x = a, B x <= b, l <= x <= u$, where ...
0
votes
0answers
62 views

Is this a quadratic programming problem?

I have $N$ unknown 2D points ${\bf x} = (x,y)$ and I want to minimize: $f({\bf x}) = \sum_{i=0}^{N-1}{(||x_{i+1} - x_i||_2 - c_i)^2}$ where c are $N-1$ known scalars. What is the simplest form that ...
2
votes
1answer
152 views

Convex optimization and linear programming please help! :)

How would I write the following as a standard form LP? Minimizing $\sum_{i=1}^n x_i + c\max(a_i-x_i)$ for $a_i \ge 0$ and what is the optimal value for when $c=n$ How to express minimize $\frac{1}{2} ...
3
votes
1answer
202 views

Optimization problem with ratio objective

I need to solve the following optimization problem $$ \text{maximize} \quad \frac{(a^T x)^2}{x^TBx+c^T|x|} \quad \text{subject to} \quad ||x||_1=1 \quad (\text{or alternatively} \quad c^T|x|=1), $$ ...
3
votes
2answers
285 views

A standard quadratic minimization problem

Consider the "Complex" Quadratic minimization problem \begin{align} \min_{\mathbb{x}\in \mathbb{C}^{N \times 1}}~\mathbf{{x}}^H\mathbf{Q}\mathbf{x}-2~\Re{(\mathbf{x}^H\mathbf{b})}+1 \end{align} ...
1
vote
0answers
73 views

Minimize a complex quadratic subject to two convex quadratic constraints

I have the following the optimization problem \begin{align} \min_{\mathbb{x}\in \mathbb{C}^{N \times 1}}~&||\mathbb{x}^H\mathbb{u}||_2^2-2*Real\{ \mathbb{x^Hu}\} \\\ ...
4
votes
1answer
245 views

How to use lagrange multipliers here?

I have a simple QP as below: $\min L(x,y) = (x-5.1)^2+y^2$ such that $(x-3)^2+y^2\geq1$ $(x-5.3)^2+y^2\geq1$ $(x-7)^2+y^2\geq1$ Intuitively, I think the optimal solution of the problem is ...
0
votes
0answers
69 views

Solving non concave quadratic function in matlab with constraints

How can I solve non concave quadratic problem in matlab with constraints. I tried using quadprog but it doesn't work
0
votes
1answer
139 views

Convex optimization problem to quadratic programming problem

Briefly, have the following problem: \begin{equation} \sum_{i = 0}^n a_i \ (max [ F_i( \bar x ), 0 ] )^2 \rightarrow min, \\\\ s.t.\\\\ A \bar x \leq b \end{equation} where $ F( \bar x ) $ is a ...
1
vote
0answers
89 views

Quadratic programming with simplex constraints

I have this quadratic function $x'Ax$ which is not convex. I want to maximize this function subject to the constraints that the solution x lies in a simplex such that $\sum_{i=1}^{n}x_i=1$. That means ...
1
vote
1answer
100 views

Issues with quadratic programming

I am trying to do a quadratic programming. I have an affinity matrix A, and I have to maximize certain function x'Ax. This is basically related to feature matching i.e matching points to labels This ...
4
votes
2answers
310 views

Analog of Simplex Method for Quadratic Programming

It happened so I need to work with an algorithm for solving QP problems. The main issue here is that I can't find any references to this algorithms (at least no references in sources in english). ...
0
votes
1answer
49 views

Feasibility of a given set of Quadratic Forms

This arises as a part of my work. Given a positive number $t$, two hermitian matrices $P_1$ and $P_2$, I am interested in knowing if a unit norm vector $z$ exists such that \begin{align} ...
2
votes
1answer
71 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
votes
2answers
115 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
votes
1answer
752 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
603 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
votes
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
vote
1answer
600 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
votes
2answers
192 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
233 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
votes
0answers
79 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 ...
1
vote
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 $$\alpha_0^2+\alpha_1^2=1$$ $$\beta_0^2+\beta_1^2=1$$ ...