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Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.

1 vote

A four-variable maximization problem

By Cauchy-Schwarz for sums (with $x_i=\sqrt{a+b}$ and $y_i=\sqrt{a+c}\sqrt{a+d}$, also, I am using cyclic sum notation): \begin{split} f(a,b,c,d)&=\sum_{\text{cyc}} \sqrt{(a+b)(a+c)(a+d)}\\&\le \left( …
Maximilian Janisch's user avatar
14 votes
3 answers
2k views

How to prove $e^x\left|\int_x^{x+1}\sin(e^t) \,\mathrm d t\right|\le 1.4$?

Related question asked by me on Math SE a few days ago: How to prove $e^x\left|\int_x^{x+1}\sin(e^t) \,\mathrm d t\right|\le 1.4$? A few days ago, somebody asked How to prove $ \mathrm{e}^x\left|\int …
Maximilian Janisch's user avatar