Tagged Questions

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Reentrant constraints in active set algorithm?

Problem definition Supposing you're trying to solve a quadratic program: $$\min_x f(x) = \frac{1}{2}x^T Q x + c^T x \\ \mbox{s.t} \, \; A x \ge 0$$ Where Q is square ($n$x$n$), positive semi ...
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Avoid evaluation of a very large matrix in non-negative matrix factorization

This is somewhere in between a math and a programming question, so please send me back to SO if you think it's off-topic. I'm implementing non-negative sparse coding, a regularized variant of ...
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What are non-orthogonal eigenvectors?

Given a symmetric matrix $A$, the maximum of the trace, $Tr(Z^TAZ)$ under the assumption that $Z^TZ=I$ occurs when $Z$ has the eigenvectors of $A$, as $Tr(U^TAU)= \lambda_1 +\lambda_2+...\lambda_ d$ ...
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Reformulating objective function of canonical correlation analysis

Given two column vectors $X = (x_1, \dots, x_n)'$ and $Y = (y_1, \dots, y_m)'$ of random variables with finite second moments, canonical-correlation analysis seeks vectors $a$ and $b$ such that the ...
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Ideas on matrix factorizations and/or transformations for $\ell_1$ minimization

I am starting with a typical $\ell_1$ basis pursuit problem: $$\min_{\mathbf{x}} \Vert \mathbf{x} \Vert_1 \quad \mathrm{s.t.} \quad \Vert \mathbf{ERx} - \mathbf{y} \Vert_2 \leq \epsilon,$$ where ...
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A minimization problem

Define $$L(w,u)=\frac{1}{2}\|w-u\|^2+\beta \left\|\frac{w}{x}\right\|,~w,u\in \Bbb{R}^n$$ where $$\frac{w}{x}=\left(\frac{w_1}{x_1},\ldots, \frac{w_n}{x_n}\right)$$ $$\|x\|=\sqrt{x_1^2+\cdots+x_n^2}$$ ...
How to show that the Hessian matrix of $G$ is positive definite?
Let $\{g_i:X\subset\mathbb{R}\rightarrow\mathbb{R};\;i=1,...,m\}$ be a linerly independet set of real functions. Given $n$ points $(x_1,y_1),...,(x_n,y_n)\in X$, consider the following function ...