用matlab编写数值优化方法（最速下降法,惩罚函数法）,具体题目如下：1.Unconstrained MinimizationMinimize following quadratic functions by resorting to the steepest descent.Use different starting points and discuss the results.

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用matlab编写数值优化方法（最速下降法,惩罚函数法）,具体题目如下：1.Unconstrained MinimizationMinimize following quadratic functions by resorting to the steepest descent.Use different starting points and discuss the results.
用matlab编写数值优化方法（最速下降法,惩罚函数法）,具体题目如下：
1.Unconstrained Minimization
Minimize following quadratic functions by resorting to the steepest descent.Use different starting points and discuss the results.
(A)\x05f(x) = 2x12 + x22 _2x1x2 + 8x1 _6x2 +5\x05
(B) f(x) = 100x12 + x22 _2x1x2 _198x1 + 99
(C) f(x) = x12 + x22 + 2x1x2 _2x1 + 1
2.Quasi-unconstrained Minimization
You are provided with two main FORTRAN programs (2D.for and 10D.for) calling a subroutine (QUASI.for).This subroutine has to be completed by you to solve quadratic unconstrained minimization problems with the steepest descent method.
First introduce in QUASI.for the same changes as in part 1.You must therefore introduce lower and upper bounds on the variables.
The following quadratic functions are considered:
(A) f(x) = 2x12 + x22 _2x1x2 + 8x1 _6x2 +5\x05\x05\x05(2D.for)
Case 1:5 > xi > -5
Case 2:5 > xi > 0
Case 3:1 > xi > -5
Case 4:1 > xi > 0
(B) (10D.for)
Case 1:10 > xi > -10
Case 2:5 > xi > -5
Case 3:5 > xi > 0
Case 4:0 > xi > -5
Case 5:10 > xi > 0
Case 6:0 > xi > -10
3.Constrained Minimization
Consider the following quadratic problem with the constrained minimization.You must solve it by developing the programs with the internal penalty method and external penalty method respectively.
Use the different the penalty factors and discuss the results.
min (x1-1)2+(x2-1)2
s.t.x1+x2-10

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