优化方法代写|Ma 630 Advanced Optimization Methods Homework 7

本次美国代写是一个高级优化方法相关的Homework

Question 1: Consider the following problem, which was also a subject of the previous
assignment:

min f(x) subject to x ≥ 0; (1)

where f : R3 ! R is defined as follows:

f(x) = max (x1)2 + (x2 −1)2 + (x3)2; (x1 −1)2 + (x2 −x1)2 + 2; −x1 + 3×2 + x3 −1:

Q1a. Formulate the master problem of the bundle method for problem (1) as a
quadratic optimization problem.

 

Q1b. Solve problem (1) by the bundle method starting from (2; 2; 2) and (1; 1; 1). To
simplify the implementation, do not remove cuts; that is, Step 5 only increases
the iteration counter. Compare with the cutting plane method.

Question 2: Consider the following problem:

max (x1 − 3)2 + (x2 − 5)2
subject to x2 1 + x2 2 ≤ 10
− 2×1 + x2 = 5:

Q2a. Formulate the quadratic penalty function. Solve problem (2) numerically, using
the quadratic penalty method; use the conjugate gradient method for solving
the unconstrained problem at each iteration.

Q2b. Solve the problem analytically using the necessary optimality conditions. Com
pare the theoretical and numerical solutions and comment on the result.

Question 3: Consider the following optimization problem:

max x1x2 + x2x3 + x1x3
subject to x1 + x2 + x3 ≤ 3
x ≥ 0:

Q3.a Is the objective function convex or concave?

Q3.b (Bonus question) Analyze problem (3) using the first and the second order
optimality conditions.

Q3.c Formulate the augmented Lagrangian function for problem (3) and determine
the parameter values for which the augmented Lagrangian function is convex.

Q3.d Solve the problem using the augmented Lagrangian method.


程序代写代做C/C++/JAVA/安卓/PYTHON/留学生/PHP/APP开发/MATLAB


本网站支持淘宝 支付宝 微信支付  paypal等等交易。如果不放心可以用淘宝交易!

E-mail: itcsdx@outlook.com  微信:itcsdx


如果您使用手机请先保存二维码,微信识别。如果用电脑,直接掏出手机果断扫描。

blank

发表评论