Question

3. a) Short questions (Please briefly jiustify your answers in each case to receive full credits) i) If we wish to minimize a function, fx.v)- 2x245x2+10, using Univariate Search method, how many searches will it take to reach the minimum and why? ii) Starting from an initial guess, Xo the minimization of the following function using Newton-Raphson method fails to work. Please explain why. f(X)-0.5x2 +2x1x2-(1/3)x +50 Note: N-R method: X- X1 - [ H(X 1)] 'Af(X), where H is Hessian matrix, Af is gradient vector] ii) Three highly nonlinear curves, fx,y), g(x.y) and h(x.y), intersect each other at a point, (x*y*) which we need to find. Formulate the above problem as an optimization problem that can be solved by an unconstrained multivariable computer optimization technique. and C = b) Suppose we wish to minimize the function, f(X) 0.5X'CX + bX+ 1, where b -CH1 .Please carry out the first using Steepest Descent optimization method starting from Xo iteration by hand and check for convergence.

Answer 1

- 2 and +S0 First we bsnd t Heissian mutrix 271 2X1 -2 X HI) 2- 2 4 2. -2-2) sdegenerde this = 4-4 -0 one csg valu zero So to woYk Newton method