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A quadratic program (QP) is an optimization problem in which the objective function is quadratic and the feasible region is a convex polytope.

2 votes
1 answer
326 views

A "nice" (but non-definite) quadratic programme

For integers $n\geq k>0$, let $f$ be the following quadratic form: $$f(x_1,\ldots,x_n)=\sum_{i=1}^n\sum_{j=0}^{k-1}x_ix_{i+j\bmod n}.$$ Is it true that the minimum of $f$ over the unit simplex is atta …
Ron P's user avatar
  • 947
2 votes
2 answers
104 views

Correlation between the first and a random position of an ergodic bit sequence

Edit: Since the geometric approach did not work, I try now another approach: phrasing the problem as a quadratic programme. Probabilistic version. Let $x=(x_1,x_2, \ldots) $ be an ergodic random seq …
Ron P's user avatar
  • 947