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Global Optimization in Hilbert Space

Boris Houska (borish***at***shanghaitech.edu.cn)
Benoit Chachuat (b.chachuat***at***imperial.ac.uk)

Abstract: This paper proposes a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. Because these run-time bounds are independent of the number of optimization variables and, in particular, are valid for optimization problems with infinitely many optimization variables, we prove that the algorithm converges to an epsilon-suboptimal global solution within finite run-time for any given termination tolerance epsilon > 0. Finally, we illustrate these results for a problem of calculus of variations.

Keywords: Infinite-dimensional optimization; Complete search; Branch-and-lift; Convergence analysis; Complexity analysis

Category 1: Global Optimization (Theory )

Category 2: Infinite Dimensional Optimization (Other )

Citation: Technical Report, October 2015

Download: [Compressed Postscript][PDF]

Entry Submitted: 08/05/2016
Entry Accepted: 08/08/2016
Entry Last Modified: 08/09/2016

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