How do I interpret the results from Multistart?

I am working on replicating results from a research paper, and I have been trying to understand the associated Matlab code. How do I interpret these results from the command window? I have been searching online how to interpret these results with no success. Thanks for the help in advance.

1 out off 1

start ms GODA

Run Local Local Local Local First-order

Index exitflag f(x) # iter F-count optimality

1 -2 5.359 53 675 137.6

2 1 0.3355 94 912 9.129e-07

3 0 3.044 100 1022 646.1

4 2 5.405 36 446 35.89

5 0 0.3355 100 974 0.003064

6 2 5.405 46 545 38.45

7 0 2.212 100 1159 46.59

8 0 0.3427 100 947 0.002296

9 2 5.407 70 930 38.73

10 0 0.3547 100 1014 0.2097

11 0 2.371 100 978 199.4

12 2 0.3456 88 837 1.892e-06

13 2 5.409 38 471 24.24

14 0 0.3404 100 981 0.4935

15 0 0.3346 100 1004 0.01332

16 2 2.68 22 358 0.2705

17 2 2.248 52 800 0.04665

18 0 1.661 100 1014 7.837

19 -2 5.423 4 90 19.48

20 2 5.402 74 859 42.38

21 0 0.3341 100 1006 0.00243

22 0 1.773 100 1004 9.132

23 -2 5.416 2 52 1642

24 -2 5.417 2 31 479

25 2 5.403 91 984 75.26

26 0 2.981 100 978 834.3

27 1 0.3355 87 861 1.341e-07

28 0 0.3497 100 978 0.07815

29 0 2.33 100 1126 271.2

30 2 5.409 55 692 34.38

31 2 5.405 71 784 38.15

32 0 0.3359 100 998 0.03016

33 2 1.564 73 810 0.3818

MultiStart stopped because maximum time was exceeded.

MultiStart called the local solver 34 times before exceeding

the clock time limit (MaxTime = 600 seconds).

14 local solver runs converged with a positive local solver exit flag.

Answer 1

[Alan Weiss]

Here is how to interpret the results. I assume that the local solver is fmincon.

• The local exitflag is the exit flag from fmincon. So in your iterative display, the first run finds no feasible point (exit flag -2). The second run has exit flag 1, a good result. Most of the exit flags are 0 or -2, meaning fmincon failed to converge to a solution. Exit flag 1 means converged to a good solution, and 2 means might have converged to a good solution.
• Local f(x) gives the objective function value at the point where fmincon stopped. You want the lowest f(x).
• Local #iter and local F-count report statistics about the convergence process.
• First-order optimality gives a measure of the quality of the solution. See First-Order Optimality Measure. A measure near 0 is good, and corresponds to exit flag 1.

Alan Weiss

MATLAB mathematical toolbox documentation

[BHH]

Thank you so very much. :)

If fmincon failed to converge to a solution does that mean that there was no good f(x) from the the run?