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# 运筹学代考 Operations Research代写

2021-11-16 12:14 星期二 所属： 作业代写 浏览：39 ## Midterm ofECEGY6233Spring2021

### Problem 1:  运筹学代考

Given f  =

4x221  + 3x222  – 4x1 x2  x1 ,  the point X0  = (-1/ 8,  0)T  ,  and the direction vector d0= – (1/ 5,  2 / 5)T

(i) Is d0 a decent direction?

(ii) Denoting g(a ) =  f (x0  + ad0 ),  find dg(1) / da ,  or equivalently, g’(1).

### Problem 2: 运筹学代考

Consider a minimum weight design problem based on plastic collapse formulated by

minimize

P = 8Mb + 8Mc

subject to M3 ≤Mb ,

M4 ≤Mc ,

M5Mc ,

2M3 – 2M4 + M5 -1120 ≤Mc,

2M3 – M4 – 800 ≤ Mb ,

2M3 – M4– 800 ≤Mc ,

Mb  ≥ 0, Mc  0,

M3  , M 4 , M 5 unrestricted in sign

Determine the plastic moment capacities Mb , M c and the plastic hinge moments M 3 , M4, Mfor the above formulation.

### Problem 3:  运筹学代考

Consider the following constrained minimization problem

minimizef = 0.01x2 + x2

subject to

g1= 25 –x1x2 ≤ 0,

g1 = 2 – x1 ≤ 0,

x1 ≥0,x≥ 0

(i)Obtain the solution graphically.

(ii)Obtain the solution using KKT condition.

(iii)Verify the sufficient conditions for optimality. 