Is it possible to use previous estimated values to improve fmincon's efficiency?

Since my objective function using numerical integration multiple times, which means it is not that smooth (actually lumpy) as other normal functions, I tried to run multiple times of optimization to make sure what I got was the "best" estimators. Now what I use is putting my first fmincon estimated function value in the new objective function as a punishment which assigns huge positive number if the objective function value in the second fmincon round is larger than the former one (since I use fmincon). And my initial value is the former estimated parameters. But still it takes a very long time (more than 20 iterations) to converge (but can get some smaller number compared to the first try). I have used parallel computation and least number of points for numerical integration.

I wonder whether someone can provide some suggestions about how to improve the algorithm so that I can use the history to improve the efficiency and speed of fmincon. Thanks.

Answer 1

[Matt J]

If you expect the solution of the new problem to change only slightly as compared to the previous problem, then you can use the solution from the previous problem as the initial guess in the new optimization.