Show that the following function is convex You may use any theorems found in the flotes. However, to show that the function

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Question 1

Use the Second Geometric Optimality Conditions to show that:

(31)T E argloc minx1 +x21(x1 — 2)2—x,  o. —x1  O. —x,  O).

All necessary working must be shown.

Question 2

Show that the following function is convex:

f:R2—R

f(x1,x,) = exp (lxii + x, I) 

You may use any theorems found in the flotes. However, to show that the function

g(x) = lxi I + ix2i is convex, it is recommended that you use the definition of convexity.

 

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