For an angle, what does it mean to be bounded away 90 degrees?

Question

Nocedal and Wright, in their book Numerical Optimization, just above (3.17), use this wording:

...the angle $\theta_k$ is bounded away from $90^\circ$,...

what does this mean?

Something that is bounded is limited in some way. A function that is bounded upwards can not take infinitely large values. Something that is bounded away from something else can not get arbitrary close to it. — mathreadler, Nov 17 '17 at 11:39

score 2 · Accepted Answer · answered Nov 17 '17 at 14:19

2

It means: there exists some $\phi>0$ such that $|\theta-90|>\phi$.

answered Nov 17 '17 at 14:19

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