Paper Info
Title
Global optimization in Hilbert space
Abstract
We propose 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 \(\varepsilon \)-suboptimal global solution within finite run-time for any given termination tolerance \(\varepsilon > 0\). Finally, we illustrate these results for a problem of calculus of variations.
Year
DOI
Venue
2019
10.1007/s10107-017-1215-7
Mathematical Programming
Keywords
Field
DocType
Infinite-dimensional optimization,Complete search,Branch-and-lift,Convergence analysis,Complexity analysis,49M30,65K10,90C26,93B40
Hilbert space,Infinite-dimensional optimization,Mathematical optimization,Global optimization,Calculus of variations,Global optimality,Optimization problem,Mathematics,Bounded function
Journal
Volume
Issue
ISSN
173.0
1-2
1436-4646
Citations 
PageRank 
References 
0
0.34
24
Authors
2
Name
Order
Citations
PageRank
Boris Houska121426.14
Benoît Chachuat212510.89