Unformatted text preview: 4. (20 points) (3) Deﬁne a convex function (on a convex set S).
_ (b) Use the deﬁnition in part (a) to show that L(m) = 23; + 1 is a convex function (on the real line). . _
(c) Given that f (3:) is a convex function (on a convex set S), for what values of
the real number a is the function h(m) = a f (I) also a convex function? ‘Show that inactive“: Mil as“; § ’
y_ mic—WM?) saucer) + (#4)}?ng
(8%“) Lﬁo<2<ﬂ+ZI—o<)7)k: g(p(x+(,PK)oy)+/ \
KLOGMF (P00h7) : ”WNW/M (”(9”ng
~2ng +d+(z»x)aa+‘/°¢ , ‘
”3 1(0<>G+(/~oz)j7+ l 21(4X+(/q<)7) MAT“? in»; aEIoZXA'U'd/ig) '5 09% +10“) ’87?
{ﬂ K20 aECMX+CF°W7I g 4(xﬁ0c)+(/‘°()78(7)) { :xa‘ﬁtk) +(1’V\)¢Wﬂ‘7} , MyﬁLUJggjé «(Am +U’QM‘77 51> CUM/30 , 0L Edi—t; 6x<0 (71% A
MMMCPWW >°J~OG>+CP09 ‘7) ngfcwvax ...
View
Full Document
 Spring '10
 Brown

Click to edit the document details