数值科学计算

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NUMERICAL OPTIMISATION TUTORIAL 2 MARTA BETCKE KIKO RUL·LAN (a)  Code backtracking line search, steepest descent and Newton’s algorithms. See Cody Courseworks for more guidance. Submit your implementation via Cody Coursework. [30pt] (b)  Apply steepest descent and Newton’s algorithms (with backtracking line search) to minimise the Rosenbrock function f(x)=100(y−x2)2 +(1−x)2. Set the initial point x0 =

NUMERICAL OPTIMISATION ASSIGNMENT 1 MARTA BETCKE KIKO RUL·LAN EXERCISE 1. Given the following function f(x,y)=2x+4y+x2 −2y2 (a)  Visualise the function and its contours. Submit your solutions via Turnitin. (b)  Calculate the contours analytically. Submit your solutions via Turnitin. (c)  Calculate the gradient analytically. Find the stationary points and classify them i.e. are them minima, maxima

EXERCISE 1. NUMERICAL OPTIMISATION ASSIGNMENT 0: EXAMPLE MARTA BETCKE KIKO RUL·LAN (a)  Write a Matlab function that implements the Rosenbrock function f(x,y)=100(y−x2)2 +(1−x)2. Be careful to implement a function that can be evaluated at many points simulta- neously. Submit your implementation via Cody Coursework. (b)  Create a two dimensional grid using Matlab’s command meshgrid. Plot