6. Minimize f 0൯൪൭) = — x2 + 217+ 2x1x2 + starting from the point xo) = (using
conjugate gradient method

(9 marks)
PART-C
7. a) Minimize f (XI, x2) = x? + x} + 60x1 subject to the constraints
— -80 2092
21+ - 120 2 0 using Kuhn-Tucker conditions.
b) What are the limitations of Kuhn-Tucker theorem? (9 marks)
8. a) What do you mean by barrier function? (3 marks)

(3 marks)
b) Minimize = (x, - + )<2 —subj.to 5 penalty function + x2 — 42 0 using
method. Use logarithmic penalty function.
(9 marks)
9. 9) State and explain Bellman's theorem in dynamic programming.
(3 marks)

b) Discuss forward and backward recursion in dyn. programming with suitable
equations. http:/'www.ktuonline.com

(9 marks)