2012/05/06 by Jingjun Han, Zhi Jin, Han, Jingjun +3
Computer Science · Engineering · Mathematics · #14Q20 #68W30 #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #B.2.4 #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #acm:14Q20 #acm:68W30 #cs.SC #math.AG #msc:14Q20 #msc:68W30
paper · pdf · doi:10.48550/arxiv.1205.1223
26 pages
openalex publication_date 2012/05/06 · arxiv created 2013/08/04 · arxiv updated 2013/08/06 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Let \xxn=(x1,…,xn) and f∈ \R[\xxn,k]. The problem of finding all k0 such that f(\xxn,k0)≥ 0 on ℝn is considered in this paper, which obviously takes as a special case the problem of computing the global infimum or proving the semi-definiteness of a polynomial. For solving the problems, we propose a simplified Brown's CAD projection operator, \Nproj, of which the projection scale is always no larger than that of Brown's. For many problems, the scale is much smaller than that of Brown's. As a result, the lifting phase is also simplified. Some new algorithms based on \Nproj for solving those problems are designed and proved to be correct. Comparison to some existing tools on some examples is reported to illustrate the effectiveness of our new algorithms.