# Tag Info

### Small quadratic programming problem - a simple Fortran code needed

John Burkardt provides parallelepiped_point_dist_3d in his geometry library. The Fortran90 version: https://people.sc.fsu.edu/~...
• 716
Accepted

### Can this simple quadratic optimization problem be turned into a simple eigenvalue problem?

At least for the second question the answer is yes. See for example Mattheij, Robert MM, and Gustaf Söderlind. "On inhomogeneous eigenvalue problems. I." Linear Algebra and its Applications ...
• 188
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### Small quadratic programming problem - a simple Fortran code needed

Your problem is a bounded variables least squares (BVLS) problem. For small instances, an active set method can quickly solve the problem. Lawson and Hanson have Fortran code for this in their book ...
• 18.9k
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### Reformulate a strictly convex QP problem containing absolute value term

\begin{align} \text{Minimize}\quad&\frac{1}{2} x^T Q x + a^T x + c^T|x| \\ \text{subject to}\quad&Gx \leq b \end{align} where $Q$ is positive definite matrix, $c^T \gt 0$ (element-wise) ...
• 191
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### Quadratic programs with rank deficient positive semidefinite matrices

To ensure this does not drown in the comments, I make it an answer. The solver used is not SeDuMi, as claimed in the question. The solver used is quadprog, and that solver (or more specifically, a ...
• 1,848

### Discrete-time Algebraic Riccati Equation (DARE) solver in C++

If you want a ten-line solution that is decently fast and stable, you can implement yourself the structured doubling algorithm: set up the coupled iteration $A_0 = A, G_0 = G = BR^{-1}B^T, H_0 = Q$ ...
• 11.8k
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### Checking positive definiteness on a hyperplane

Instead of e = eig(N'*A*N);, you can use [R,p]=chol(N'*A*N);, and test for p==0. Matlab ...
• 571

### How to ensure the numeric value is always positive in Optimization Python?

Consider a variable transform. Assuming you care about the individual entries of $x$ and not something like its determinant, you can transform the $x_i$ such that the new variable $y_i$ is not bounded ...
Accepted

### Is solving QP easier than a QCQP with linear objective?

Quadratically constrained problems are fundamentally more complicated than linearly constrained problems because the feasible set is not necessarily convex (unless, of course, you are specific about ...
• 56.2k
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### Which optimization method can be used to do the following?

Despite my comment, I think you can find $\tilde{D}$ that contains the noise term as well. You have this equation: $$-M^{T} \tilde{D} M \phi(t) = -M^{T} D M \phi(t) + W(t)$$ Where $W(t)$ is the ...

Applying the transformation you suggested, we get: $$\min_{y \in\{0,1\}^n} (\mathbf{1}-y)^TP(\mathbf{1}-y)$$ $$\mathrm{s.t.}\;\;w^T(\mathbf{1}-y)\geq c\, ,$$ where $n$ is the dimension where $x$ ...
• 131

• 18.9k
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### Approximating solutions to quadratic recurrence boundary value problem

Newton-type methods are standard methods for solving system of nonlinear equations numerically. To make sure they can handle this, I tried solving your problem with NLsolve.jl in julia, and it seems ...
• 11.5k

Your conjecture can not be correct, for two purely formal reasons: In $x^T Q x$, if you multiplied this out as a sum $\sum_i \sum_j Q_{ij}x_ix_j$, every term in the sum is the product of two entries ...
• 56.2k

• 470

### Solving a parameter estimation problem using trajectory optimization

I am a bit confused as to your characterization of constraints. Equation $(1)$ is not a constraint. It is the model that generated the time series data you are trying to fit. You then try to find the ...
• 2,926
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### Numerical Simulation of a Quadratic MIP with a highly rational term

Getting an exact solution via brute force I'll try to circle back later to formulate this as a MIP, but your problem as stated is small enough that you can just brute force the solution. For instance, ...
• 4,021
Accepted

### Can this problem be solved using convex optimization?

This is not a convex problem. In fact, I don't think it even has a problem. Think about the special case where $x\in{\mathbb R}^1$, then your problem has the form \begin{align} \max & \quad \...
• 56.2k
1 vote

### Project to nearest point on convex polytope

Assume that $y$ is not in the polyhedron (it is easy to check whether it is, and we know that the distance is zero in that case). If $y$ is outside then the closest point will be on the surface of the ...
• 2,831
1 vote
Accepted

### Why am I getting this DCPError?

cvxpy's rules for disciplined convex programming are listed here. Notably, it states that: The DCP rules require that the problem objective have one of two forms: Minimize(convex) ...
• 4,021
1 vote
Accepted

### Minimize squared error of linear function

Your problem is still a linear least squares problem. You can write $\Psi(x)$ as $\Psi(x)=\| Hx - g \|_{2}^{2}$ where $H=\left[ \begin{array}{c} I \\ M \end{array} \right]$ and \$g=\left[ \...
• 18.9k

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