interesting topic

The link provided below will provide some insight into this.

Best regards,

Conference Paper Efficient Bayesian inference methods via convex optimization...

Thank you @muraleedharan

Dear Abdullahi Abbas Adam

In Bayesian optimization, the cost-function is assumed to vary idealistically within a predicted, preferred and restricted bound around the observed value. whereas, the real-solution might be realistically far outside of the limited region of search and inspection. Therefore, the optimum solution found based on Bayesian optimization could be quite unsatisfactory, and with large error.

Convex optimization, usually is used for finding the extremum of a convex cost-function. But the convex cost-functions are limited in range, and in practical applications, the cost-function is usually non-convex, hence convex-optimization fails to predict the extremum in its global sense. Moreover, for non-convex cost-functions, convexification is an option, but convexification, is actually the quasi-linearization of a function in sub-intervals and then seeking the extremum. This could drastically ignore the real behavior of the function in a large domain of search, hence failing to find the global optimum, and only surrenders the local optimum.

Thank you very much for this valuable input Saeb AmirAhmadi Chomachar . This is very interesting and impressive. Please could you give me some references for further reading?

Does Bayesian and Convex optimizations approaches use design of experiment? Are they also multiple regression base? Do they employ any artificial Intelligence or a kind of response surface?

Thank you one more time.

Dear Abdullahi Abbas Adam

Thank you for the interest. Unfortunately, I have not any specific paper to suggest you in this area of research. However, a simple Google search and also a search in Google scholar, could present you many papers on the subject of Bayesian optimization and convex optimization. Please see the screenshot which I have attached to this comment for your perusal.

Update: Bayesian optimization could be used when function evaluation is expensive, hence only a black-box model of the function is available. Therefore, it is not dependent sensitively on the function and precise model, in other words it is robust, as robust control.

Regards,

Saeb AmirAhmadi Chomachar

Dear Abdullahi Abbas Adam

Please search in Google these keywords:

occupation measure, Markov chain, optimal control, stochastic optimal, inverse optimal, inverse reinforcement learning, convex optimization.

These are related to each other.

I came across a paper in Google search, I cite here as:

Nonlinear optimal control: a numerical scheme based on occupation measures and interval analysis

Article Nonlinear optimal control: a numerical scheme based on occup...

Very important topic.

The most important thing is to read the sources related to this topic