2017/07/28 by Jiawang Nie, Nie, Jiawang, Jinling Zhao +1
Business, Management and Accounting · Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Facility Location and Emergency Management #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1707.09429
openalex publication_date 2017/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations for representing the intersection of the sets. Properties of the semidefinite relaxations are studied. Based on that, a semidefinite relaxation algorithm is given for solving the split feasibility problem. Under a general condition, we prove that: if the split feasibility problem is feasible, we can get a feasible point; if it is infeasible, we can obtain a certificate for the infeasibility. Some numerical examples are given.