query: Prove formally that multivariate function has global extrema
positive_passages.docid: 154085
positive_passages.text: $\sum a_i \ln(b_i) \leq \sum a_i \ln(a_i)$ with $\sum a_i = \sum b_i = 1$
negative_passages.docid: 33308
negative_passages.text: Unique local extremum is absolute extremum for continuous functions
negative_passages.docid: 108997
negative_passages.text: Continuous functions that attain local extrema at every point
negative_passages.docid: 4498
negative_passages.text: Proof that $\|fx\| \leq \|f\|\cdot\|x\|$
negative_passages.docid: 146656
negative_passages.text: Multivariate Application of Slutsky's lemma
negative_passages.docid: 126698
negative_passages.text: measurability of a function -equivalent conditions
negative_passages.docid: 77217
negative_passages.text: Proof that a coordinate-wise convex function is convex?
negative_passages.docid: 55679
negative_passages.text: Does there exist a continuous function from [0,1] to R that has uncountably many local maxima?
negative_passages.docid: 107686
negative_passages.text: Proof that the gamma function is an extension of the factorial function
negative_passages.docid: 155004
negative_passages.text: Maximal points on an $n$-dimensional ellipsoid
negative_passages.docid: 19658
negative_passages.text: $\max_{t\in[0,T]}|x(t)|^2 \le |x(0)|^2e^{\int_0^T|y|^2\,\mathrm ds}.$ using gronwall's lemma?
negative_passages.docid: 88271
negative_passages.text: Prove the exsistence of 3 zero points of a function
negative_passages.docid: 94231
negative_passages.text: Prove that a non-empty closed convex $S$ has an extreme point iff it does not contain any line
negative_passages.docid: 43419
negative_passages.text: At unique critical point, does local max imply global max?
negative_passages.docid: 14079
negative_passages.text: On the proof that every positive continuous random variable with the memoryless property is exponentially distributed
negative_passages.docid: 151302
negative_passages.text: If $X$ and $Y$ are independent random variables, with $Z = \min(X,Y),$ prove that $Z^2\sim\chi^2(1),$
negative_passages.docid: 84697
negative_passages.text: Show that if $|f(z)| \leq M |z|^n$ then $f$ is a polynomial max degree n