Title：On Difference of SOS Decompositions and Difference of SOS Convex Decompositions for Polynomials

Speaker：牛一帅  (教授，上海交通大学)

Time：2018年5月8日    下午 16:30-17:30

Room：东区管理科研楼   数学科学学院1518室

Abstract： We propose in this paper some decomposition methods for reformulating any multivariate polynomial into DSOS (Difference of Sums-Of-Squares) and DSOSC (Difference of Sums-Of-Squares Convex) polynomials. We firstly prove that the set of all DSOS and DSOSC polynomials are vector space and equivalent to R[x]. Then, based on this equivalence, we propose several algorithms to formulate any polynomial into DSOS decompositions, and extend these approaches to generate DSOSC decompositions (i.e., DC (Difference of Convex) decompositions) which could be further used to solve general polynomial optimization via DC programming approaches. Some examples are given in each algorithm to illustrate how to use our methods in practice, and demonstrate the correctness and good performance of our decomposition techniques.