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Results tagged with nonlinear-optimization
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user 20598
Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.
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Maximize $f(0)+\cdots+f(n-1)$ subject to $f(x)f(y) + f(x+y) \leq 1$
Suppose $f:\mathbf{N} \to [0,1]$ satisfies $$f(x)f(y) + f(x+y)\leq 1\qquad(1)$$ for all $x,y$. Let $$d_n = \frac{1}{n} \sum_{x=0}^{n-1} f(x).$$ It is easy to prove that $$\limsup d_n \leq 1/\varphi,$$ …
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