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Results tagged with nonlinear-optimization
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user 11919
Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.
21
votes
Accepted
Prove that this expression is greater than 1/2
Let
$$f(x,y):=4x^{2}+4y^{2}-4xy-4y+1 + \frac{4}{\pi^2}\Bigl(
\sin^{2}(\pi x)+ \sin^{2}(\pi y) + \sin^{2}(\pi y-\pi x) \Bigr).$$
I will show that
$$\min_{0\leq x\leq y\leq 1}f(x,y)=\min_{0\leq x\leq 1/ …
- 95.7k
11
votes
Accepted
Min problem on integers
Let us denote
$$\sigma_\ell:=\sum_{i=1}^\ell q_i\qquad\text{and}\qquad\tau_\ell:=\sum_{i=\ell+1}^s\frac{1}{q_i}.$$
Then
$$\prod_{\ell=1}^{s-1}\left(\frac{q_\ell}{q_{\ell+1}}\cdot\frac{\sigma_{\ell+1}} …
- 95.7k