Wednesday, 16:15 - 16:40 h, Room: H 2053

 

Spencer Schaber
Convergence order of relaxations for global optimization of nonlinear dynamic systems

Coauthor: Paul I. Barton

 

Abstract:
Deterministic methods for global optimization of nonlinear dynamic systems rely upon underestimating problems for rigorous bounds on the objective function on subsets of the search space. Convergence order of numerical methods is frequently highly indicative of their computational requirements, but has not yet been analyzed for these methods. We analyzed the convergence order of the underestimating problems to the original nonconvex problem for one method of nonlinear global dynamic optimization. We found that the convergence order of the underestimating problem is bounded below by the smallest of the convergence orders of the methods used to compute (i) the bounds for the states as well the convex/concave relaxations of the (ii) vector field, (iii) initial condition, and (iv) objective function in terms of the state variables. We compared the theoretical convergence order result to empirical results for several optimal-control and parameter-estimation problems and found that the bounds were valid for all problems and sharp for some. We confirmed that empirical convergence order is highly correlated with the CPU time for full global dynamic optimization.

 

Talk 3 of the invited session Wed.3.H 2053
"Nonconvex optimization: Theory and algorithms" [...]
Cluster 9
"Global optimization" [...]

 

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