what is the best way to search or interrogate an initial solution of a non-linear optimization problem you (strongly) believe is close to the optimal solution?
is there a better approach or strategy than to incrementally or iteratively increase a band of floors and ceilings around the initial solution, until this no longer has any effect? this approach should be better than starting with a wide band around the initial solution from the onset?
Not for the chance of plugging a paper written by me and a colleague, but the link below is a thorough analysis of what optimality means, and - in addition - what near-optimality means!
http://www.math.chalmers.se/~mipat/LATEX/OR_final_single.pdf
The above is the last preprint - here is the permanent link to Oper Res:
Article Global Optimality Conditions for Discrete and Nonconvex Opti...
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