1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
|
//Example where user provides hessian
function y=f(x)
y=x(1)*x(2)+x(2)*x(3);
endfunction
//Starting point, linear constraints and variable bounds
x0=[0.1 , 0.1 , 0.1];
A=[];
b=[];
Aeq=[];
beq=[];
lb=[];
ub=[];
//Nonlinear constraints
function [c,ceq]=nlc(x)
c = [x(1)^2 - x(2)^2 + x(3)^2 - 2 , x(1)^2 + x(2)^2 + x(3)^2 - 10];
ceq = [];
endfunction
//Hessian of the Lagrange Function
function y= lHess(x,obj,lambda)
y= obj*[0,1,0;1,0,1;0,1,0] + lambda(1)*[2,0,0;0,-2,0;0,0,2] + lambda(2)*[2,0,0;0,2,0;0,0,2]
endfunction
//Options
options=list("MaxIter", [1500], "CpuTime", [500], "Hessian", lHess);
//Output
//Optimal Solution Found.
// hessian =
//
// 1.4142136 1.72D-322 2.12D-314
// 1. 0. 5.82D+252
// 1. 1.4142136 1.
// gradient =
//
// 2.236068 - 3.1622776 2.236068
// lambda =
//
// lower: [0,0,0]
// upper: [0,0,0]
// ineqlin: [0x0 constant]
// eqlin: [0x0 constant]
// ineqnonlin: [4.545D-09,0.7071068]
// eqnonlin: [0x0 constant]
// output =
//
// Iterations: 23
// Cpu_Time: 0.164
// Objective_Evaluation: 24
// Dual_Infeasibility: 6.124D-08
// Message: "Optimal Solution Found"
// exitflag =
//
// 0
// fopt =
//
// - 7.0710678
// xopt =
//
// - 1.5811388
// 2.236068
// - 1.5811388
//Calling Ipopt
[xopt,fopt,exitflag,output,lambda,gradient,hessian] =fmincon(f, x0,A,b,Aeq,beq,lb,ub,nlc,options)
|
