2013/04/16 by Vaithilingam Jeyakumar, V. Jeyakumar, Jeyakumar, Vaithilingam +6
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical Methods and Algorithms #Optimization and Control (math.OC) #Polynomial and algebraic computation #math.OC
paper · pdf · doi:10.48550/arxiv.1304.4552
openalex publication_date 2013/04/16 · arxiv created 2013/07/04 · arxiv updated 2013/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the class of polynomial optimization problems inf \f(x):x∈ K\ for which the quadratic module generated by the polynomials that define K and the polynomial c-f (for some scalar c) is Archimedean. For such problems, the optimal value can be approximated as closely as desired by solving a hierarchy of semidefinite programs and the convergence is finite generically. Moreover, the Archimedean condition (as well as a sufficient coercivity condition) can also be checked numerically by solving a similar hierarchy of semidefinite programs. In other words, under reasonable assumptions the now standard hierarchy of SDP-relaxations extends to the non-compact case via a suitable modification.