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Obtain approximate Hessian using FindMinimum

According to the documentation, when FindMinimum is told to use the method "QuasiNewton" on a unconstrained problem, it uses the ...
596 views

Differentiating functions of vectors/matrices?

I'm dealing with derivatives of scalar functions of matrices and wondering if Mathematica can help me here. The standard approach of expanding it in terms of components is cumbersome. As an ...
1k views

How can I complete a correlation matrix with missing values?

I would like to complete a correlation matrix with missing entries, such that the resulting matrix is positive semi-definite. Say I want to find some x and some y in the next matrix that satisfy ...
861 views

Indicate minimal path sum

Described on the page: http://www.mathblog.dk/project-euler-81-find-the-minimal-path-sum-from-the-top-left-to-the-bottom-right-by-moving-right-and-down/ It is an example of the solution indicated in ...
830 views

Is there any fast way to solve a quadratic matrix equation in Mathematica approximately?

Let the square nonsingular matrix $M$ is a given convergent matrix. What are the best scalar values for $\alpha$ and $\beta$ (in the real numbers domain), at which the following quadratic matrix ...
818 views

Maximization in Mathematica using matrix and vector notation

I am trying to solve a simple maximization problem in Mathematica, using matrix and vector notation. ...
1k views

FindMaximum “is not a real number at” nrnum problem

I'm experiencing a problem using FindMaximum that I don't understand (due to my newbie knowledge of Mathematica's syntax). That is, FindMaximum sometimes returns a (correct) answer, but sometimes ...
830 views

Optimizing functions taking matrix arguments

I'm looking for general information on how to optimize matrix valued functions, I have the following function I'm looking to maximize (or figure out if this is possible at all). ...
111 views

Suppose that $A$ is an $n \times n$ matrix, and I have observed some entries of $A$, say, $A_S$ ($A$ restricted on $S$) for some subset $S$ in $\{1,...,n\} \times \{1,...,n\}$. I want to know if it's ...
318 views

Optimize a parametric matrix to get a lowest possible eigenvalue

This question is a followup of Plot the lowest eigenvalues of a parametric matrix Now I can get the lowest eigenvalue LowEign(t) of the matrix for a given t numerically. When I plot the LowEign ...
213 views

Defining a function for the construction of a bordered hessian

I think in Mathematica the omission of a function that can create a bordered matrix. This code works ...
200 views

83 views

Which method to use for finding maximum without actually computing optimization function explicitly?

I am new to Mathematica and I am currently working on an optimization problem. The optimization function that I have easy to calculate for some assignment of variable but it is very difficult to ...
138 views

NMaximize with matrix input

I defined function f[x_, fixed_] := {...}. Here x is an $M\times N$ matrix. I want to maximize $f$ with respect to $x$. I have ...
86 views

An optimization problem involving the calculation of MatrixRank as a constraint

I am dealing with an optimization problem that involves the rank of a matrix as a hard constraint. I am starting with this simple example ...
41 views

How can I specify the region for every variable simultaneously in NMinimize?

I want to use NMinimize to find the unknown unitary matrix that solves a (possibly nonlinear) matrix equation. For example, the one that transforms the Pauli matrix ...
I need to come up with a solution for a rather, odd situation. Let's say I have an $M \times N$ matrix called ${\bf A}$, and I would like to solve it for ${\bf x}$ where \$b_1 \le {\bf A} {\bf x} \le ...