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Here's a problem I'm trying to solve.

Given a planar piecewise linear and circular curve (ie. a curve consisting of line and circular arc segments) that represents the path of a particle; a set of rules for traversing the two types of curve segments as well as the transitions between the segments by my particle and finding the travel time (ie the speed is not constant); bounds on jerk/acceleration/velocity

I want to find another planar piecewise linear and circular curve satisfying a set of criteria (described non-rigorously just to provide some context) such as:

- closeness to the original curve

- minimizing the total travel time

- minimizing the jerk experienced by particle

If there are more than one curves satisfying my constraints that is OK.

Which type of optimization does this problem fall under?

I'm looking for some guidance so that I could start reading up on the relevant topics/mathematical tools. I can update the description with more details if necessary.

Thanks!