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Suppose, we have a linear program and an optimal solution to it. Suppose now, we get a new constraint. We want to obtain an optimal solution to the given linear program extended by that new constraint....

Given a p.s.d. matrix $A$, one may want to find: $$ \max_x x^t A x \mbox{ such that } x \mbox{ has entries }1 \mbox{ or } {-1}. $$ This hard problem has a well known relaxation based on the so called ...

Are there any efficient algorithms/heuristics for basis pursuit for exponentially large matrices? That is $$\begin{array}{ll} \underset{x \in \Bbb R^n}{\text{minimize}} & \lVert x \rVert_0\\ \text{...

I am working on a binary optimization problem. So far I have derived the following constraint functions. \begin{align} \begin{bmatrix} \left( P + \sum_{i=1}^n (\sum_{j=1}^n x_{i, j} \alpha_j) e_i e_i^...

I have $f(x)$ with $x \in [0,1]$ and $f(x)$ is convex, then, under which conditions discrete function which is defined as $f(x_h)$ on discrete subset of $[0,1]$, for example, $x_h \in \{0, h, 2h, \...