I invented a new objective function of an optimal programming which will lead to a new solving approach. Can I file a patent application on a new objective function for an optimal programming?
George and Eric, the current objective function uses weighted least square to formulate the optimal problem. But there are a lot of problems caused by current objective function: cannot guarantee to converge, cannot reach the true state of the variables, etc. We developed a new objective function which overcomes those problems. But we do not want to disclose the details of how to solve this new objective function. We have a concern that it will be a big and costy issue if somebody develops a product according to our formulation and approach of solution. For example, in China, the copyright is not respected and not well practiced. International companies are very hard or impossible to win a lawsuit in China if a Chinese company develops the same product according to our patent. We are originally from China and well understand the situations in China. In summary, we want to protect the objective function but not the detailed solving approach. Do you think this is a good idea? Thanks a lot.
Not to be crass about your possibly brilliant work, but it is unlikely your invention is entirely dissimilar to work published in an academic journal of programming, statistics, mathematics, economics, etc. Patenting a method of production based on some theoretical usage seems dodgy, unless it is clear how your optimization method will be implemented in a process.
If the plan is to patent some optimization algorithm so you can use it exclusively in consulting work, I'd question the merits of a patent (particularly if my first sentence holds true; I know of numerous academics who do consulting work based on research but no patent). However, big tech companies have filed many patents for algorithms designed to solve niche problems; the patent documents state at least generally how the proprietary method is implemented in "production". Sounds like you need to do some research.
Also I agree with the other comments: you should delete your "answer" and move the important parts to your "question" using the edit function.