  


A Perturbed Sums of Squares Theorem for Polynomial Optimization and its Applications
Masakazu Muramatsu (muramatucs.uec.ac.jp) Abstract: We consider a property of positive polynomials on a compact set with a small perturbation. When applied to a Polynomial Optimization Problem (POP), the property implies that the optimal value of the corresponding SemiDefinite Programming (SDP) relaxation with sufficiently large relaxation order is bounded from below by $(f^¥ast  ¥epsilon)$ and from above by $f^¥ast + ¥epsilon (n+1)$, where $f^¥ast$ is the optimal value of the POP. We propose new SDP relaxations for POP based on modifications of existing sumsofsquares representation theorems. An advantage of our SDP relaxations is that in many cases they are of considerably smaller dimension than those originally proposed by Lasserre. We present some applications and the results of our computational experiments. Keywords: Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Category 2: Convex and Nonsmooth Optimization (Convex Optimization ) Category 3: Nonlinear Optimization (Quadratic Programming ) Citation: Download: [PDF] Entry Submitted: 03/29/2013 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  