(a) Identifying whether a function is a convex function is useful because a convex function's local minimum has the nice property that it has to be the global minimum. Please select all functions below that are convex functions. Note dom(f ) denotes the domain of the function f. Select all that apply: Of (x) =x³ + 3x+ 7, domf ) =R Of (x) = log x, domf) =R,. (the set of positive real numbers) Of (x) =|x| , domf ) =R Of (x) =2-x, domf) =R Of =||x|3, domf ) =R" O None of the above.
(a) Identifying whether a function is a convex function is useful because a convex function's local minimum has the nice property that it has to be the global minimum. Please select all functions below that are convex functions. Note dom(f ) denotes the domain of the function f. Select all that apply: Of (x) =x³ + 3x+ 7, domf ) =R Of (x) = log x, domf) =R,. (the set of positive real numbers) Of (x) =|x| , domf ) =R Of (x) =2-x, domf) =R Of =||x|3, domf ) =R" O None of the above.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(a)
Identifying whether a function is a convex function is useful
because a convex
function's local minimum has the nice property that it has to be the global minimum. Please select all
functions below that are convex functions. Note dom(f ) denotes the domain of the function f .
Select all that apply:
Of (x) =x3 + 3x + 7, domf ) =R
Of (x)
Of (x) =|x| , domf ) =R
Of (x) =2-X, domf) =R
Of =||x|, domf) =R"
log x, domf) =R,. (the set of positive real numbers)
O None of the above.
(b)
Typically we can solve linear regression problems in two ways.
One is through
direct methods, e.g. solving the closed form solution, and the other is through iterative methods (gradi-
ent descent). Consider a linear regression on data (X, y). We assume each row in X denotes one input
in the dataset. Please select all correct options.
Select all that apply:
O If the matrix X' x is invertible, the exact solution is always preferred for solving the solution
to linear regression as computing matrix inversions and multiplications are fast regardless of
the size of the dataset.
O Assume N is the number of examples and M is the number of features. The computational
complexity of N iterations of batch gradient descent is O(MN ).
O The computational complexity of the closed form solution is linear in number of parameter-
s/features.
O None of the above.
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