With a nonlinear optimization problem, would limiting the full coefficient set of x coefficients to y coefficients, with y < x, constitute searching in specific sub regions?
The remaining coefficients are set/ rendered as constants
You are not making sense. Why do you not buy a basic book on nonlinear optimization?
Here are some books on basic stuff on the topic, with well-explained examples and a theory to back them up:
Bazaraa, Sherali, and Shetty, Nonlinear Optimization, 3/e, Wiley
Griva, Nash, and Sofer, Linear and Nonlinear Optimization, 2/e, SIAM Press
Luenberger, Linear and Nonlinear Programming, 3/e, Springer
Bertsekas, Nonlinear Programming, Athena
Ruszczynski, Nonlinear Optimization, Princeton University Press
Perhaps you have a library nearby that have some of them. As you can see there are several editions of some of them - of course the advice is to buy the newest version.
You really need to start by looking at what *optimality* means, and how the basic methods are based on trying to achieve a vector in R^n with the right characteristic. We refer to them often as being "stationary points" or "vectors that satisfy the Karush-Kuhn-Tucker (KKT) conditions".
You will see that such methods are most often superior to metaheuristics. Not only because there is a solid theory behind them - they are typically better in practice.
@Michael,
See my response to your reply to my other question, that you posted today.
My problem is non convex nonlinear.
I have a basic understanding of convex optimization. I am more new to non-convex optimization based on evolutionary algorithms.
I can code and have maths education, but i am not a mathematician.
back to my optimization problem, If i provide my optimization problem with a good initial solution, it fails to improve on it still, by unpacking it and inflating it.
The problem is too nonlinear. The algorithm scans over and misses the better solutions.
I am looking for a "cutting" strategy, to cut up the solution space, as a way to force the algorithm to look more closely, by confining it to certain sub regions at a time.
At present, limiting the coefficients the algorithm can change, and setting the other coefficients as constants seem to work/ help.
I find better solutions this way, and can walk to better solutions this way.
I should probably study evolutionary algorithms aimed at non convex optimization, but am reluctant to go to that depth/ level of detail.
Would much rather partner with a mathematician.
Currently i am trying to see how far i get without going into the details of evolutionary algorithms.
If i hit a dead end, i will
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