  


Global Optimization in Hilbert Space
Boris Houska (borishshanghaitech.edu.cn) Abstract: This paper proposes a completesearch algorithm for solving a class of nonconvex, possibly infinitedimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worstcase runtime bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. Because these runtime 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 epsilonsuboptimal global solution within finite runtime for any given termination tolerance epsilon > 0. Finally, we illustrate these results for a problem of calculus of variations. Keywords: Infinitedimensional optimization; Complete search; Branchandlift; 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 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  