最优化理论与方法 试题2007e.pdf

Final Examination of Optimal Theory and Methods Name Score Notice ： Please write all the answers on the answer sheet. 1. Answer the following questions （10 points） （1）List four methods to solve one dimensional optimal problems. （2 ）List four methods to solve non-constrained multi-dimensional optimal problems. （3 ）List four methods to solve constrained multi-dimensional optimal problems. （4 ）List two methods to solve optimal problems by using the gradient. （5 ）List one method to solve optimal problems by using Hessian array. 2. Use simplex method to solve the following LP problem. （10 points） ( ) max f x 6x1 −3x2 +3x3 2 + ≤8 ⎧x1 x2 ⎪ −4x −2x +3x ≤14 ⎪ 1 2 3 ⎨ s.t. −2 + ≤18 x x x ⎪1 2 3 ⎪ ≥0 j 1, 2, 3 x ⎩j 3. Use 0.618 method to find the minimum point with a object function of ( ) 2 1 f x x −x − . List the results of first four steps. The region is [ 0, 1.2 ]. 2 （10 points） 4. Use Newton method to find the minimum value of object function ( ) 2 2 f x x1 +25x 2 . （5 points ） 1 T ( Note: take x0 ＝[2，2] ，and perform iteration once) 5. Use interior-point penalty function method to solve the following problem. minf (x) ＝ax － ） k s.t. g(x) ＝b －x ≤0 （Note ：take r ＝10 ） （5 points ） k