Sunday, June 6, 2021

Considerations for Practical Problem Formulation

 When writing guidance algorithms or optimization routines (or reading papers about them), I tend to see best results come from asking these questions. Some of them are redundant, but can apply differently at different scales. 

  • How can I simplify the formulation?
  • Can I get away with a bad initial guess?
  • Can I abstract the complicated parts to a look up table and then run a simplified routine over this with a new initial condition?
  • What methods will provide a reliable and  efficient implementation?
  • Is the problem formulation dynamically feasible?
  • Can this be fast and or parallelizable? 
  • Can I separate the problem into disjoint components and solve for each part separately and or in a parallel fashion?
  • How do I take advantage of new frames or new mappings to construct a minimal dynamical representation?
  • How does this new problem scale? 
  • How does this problem linearize, how many orders must I include to provide an accurate representation of the nonlinear dynamics?
  • Are there ways to relax some constraints of the problem?
  • What methods will provide the fastest solution? Is it possible to pose the problem in that framework?

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