University COVID-19 update

The University of Waterloo is constantly updating our most Frequently Asked Questions.

Questions about buildings and services? Visit the list of Modified Services.

Please note: The University of Waterloo is closed for all events until further notice.

Special Seminar - Yi-Shuai NiuExport this event to calendar

Thursday, February 28, 2019 — 3:30 PM EST

Title: Difference-of-SOS and Difference-of-Convex-SOS Decomposition Techniques for Polynomials

Speaker: Yi-Shuai Niu
Affiliation:

SJTU-Paristech & Maths department Shanghai Jiao Tong University

Room: MC 5501

Abstract:

We are interested in polynomial decomposition techniques for reformulating any multivariate polynomial into difference-of-sums-of-squares (DSOS) and difference-of-convex-sums-of-squares (DCSOS) polynomials. Firstly, we prove that the set of DSOS and DCSOS polynomials are vector spaces and equivalent to the set of real valued polynomials R[x]. We also show that the problem of finding DSOS and DCSOS decompositions are equivalent to semidefinite programs (SDPs). Then, we focus on establishing several practical algorithms for DSOS and DCSOS decompositions with and without solving SDPs. Moreover, the DCSOS decomposition is indeed a difference-of-convex (DC) decomposition for polynomials which helps to reformulate any polynomial optimization into DC program, the later one can be solved by an efficient DC algorithm - DCA. Some numerical examples illustrate the good performance of our methods.

Location 
MC - Mathematics & Computer Building
5501
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

S M T W T F S
30
31
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1
2
3
  1. 2020 (89)
    1. September (11)
    2. August (11)
    3. July (17)
    4. June (11)
    5. May (6)
    6. March (11)
    7. February (11)
    8. January (11)
  2. 2019 (167)
    1. December (5)
    2. November (15)
    3. October (18)
    4. September (15)
    5. August (9)
    6. July (17)
    7. June (18)
    8. May (16)
    9. April (9)
    10. March (24)
    11. February (13)
    12. January (8)
  3. 2018 (138)
  4. 2017 (103)
  5. 2016 (137)
  6. 2015 (136)
  7. 2014 (88)
  8. 2013 (48)
  9. 2012 (39)
  10. 2011 (36)
  11. 2010 (40)
  12. 2009 (40)
  13. 2008 (39)
  14. 2007 (15)