  


Moment methods in energy minimization: New bounds for Riesz minimal energy problems
David de Laat(maildaviddelaat.nl) Abstract: We use moment methods to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate the infinite dimensional optimization problems in this hierarchy by block diagonal semidefinite programs. For this we develop the necessary harmonic analysis for spaces consisting of subsets of another space, and we develop symmetric sumofsquares techniques. We compute the second step of our hierarchy for Riesz senergy problems with five particles on the 2dimensional unit sphere, where the s=1 case known as the Thomson problem. This yields new sharp bounds (up to high precision) and suggests the second step of our hierarchy may be sharp throughout a phase transition and may be universally sharp for 5particles on the 2sphere. This is the first time a 4point bound has been computed for a continuous problem. Keywords: Thomson problem, Riesz senergy, 4point bounds, semidefinite programming, Lasserre hierarchy, harmonic analysis on spaces of subsets, invariant polynomials Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Category 2: Infinite Dimensional Optimization (Semiinfinite Programming ) Category 3: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: 10/2016 Download: [PDF] Entry Submitted: 10/18/2016 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  