Low-Rank Semidefinite Programming: Theory and Applications

2016 ◽  
Vol 2 (1-2) ◽  
pp. 1-156 ◽  
Author(s):  
Alex Lemon ◽  
Anthony Man-Cho So ◽  
Yinyu Ye
Keyword(s):  
Semidefinite Programming ◽  
Low Rank ◽  
Programming Theory

Low-Rank Semidefinite Programming: Theory and Applications

2016 ◽  
Author(s):  
Alex Lemon ◽  
Anthony Man-Cho So ◽  
Yinyu Ye
Keyword(s):  
Semidefinite Programming ◽  
Low Rank ◽  
Programming Theory

scholarly journals Low-rank exploitation in semidefinite programming for control

2011 ◽  
Vol 84 (12) ◽  
pp. 1975-1982 ◽  
Author(s):  
Rikard Falkeborn ◽  
Johan Löfberg ◽  
Anders Hansson
Keyword(s):  
Semidefinite Programming ◽  
Low Rank

scholarly journals Low-Rank Semidefinite Programming for the MAX2SAT Problem

2019 ◽  
Vol 33 ◽  
pp. 1641-1649
Author(s):  
Po-Wei Wang ◽  
J. Zico Kolter
Keyword(s):  
Semidefinite Programming ◽  
State Of The Art ◽  
Search Algorithm ◽  
Low Rank ◽  
Search Methods ◽  
Maximum Satisfiability ◽  
Satisfiability Problems ◽  
Theoretical Tool ◽  
Recent Approach ◽  
Programming Techniques

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum satisfiability problems, but their application has traditionally been very limited by their speed and randomized nature. Our approach overcomes this difficult by using a recent approach to low-rank semidefinite programming, specialized to work in an incremental fashion suitable for use in an exact search algorithm. The method can be used both within complete or incomplete solver, and we demonstrate on a variety of problems from recent competitions. Our experiments show that the approach is faster (sometimes by orders of magnitude) than existing state-of-the-art complete and incomplete solvers, representing a substantial advance in search methods specialized for MAX2SAT problems.

Low-rank quadratic semidefinite programming

2013 ◽  
Vol 106 ◽  
pp. 51-60 ◽  
Author(s):  
Ganzhao Yuan ◽  
Zhenjie Zhang ◽  
Bernard Ghanem ◽  
Zhifeng Hao
Keyword(s):  
Semidefinite Programming ◽  
Low Rank ◽  
Quadratic Semidefinite Programming

scholarly journals A Relaxed Interior Point Method for Low-Rank Semidefinite Programming Problems with Applications to Matrix Completion

2021 ◽  
Vol 89 (2) ◽  
Author(s):  
Stefania Bellavia ◽  
Jacek Gondzio ◽  
Margherita Porcelli
Keyword(s):  
Semidefinite Programming ◽  
Interior Point ◽  
Interior Point Method ◽  
Matrix Completion ◽  
Point Method ◽  
Low Rank ◽  
Computational Results ◽  
First Order ◽  
Completion Problems ◽  
Primal And Dual

AbstractA new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal solution, a special nearly low-rank form of all primal iterates is imposed. To accommodate such a (restrictive) structure, the first order optimality conditions have to be relaxed and are therefore approximated by solving an auxiliary least-squares problem. The relaxed interior point framework opens numerous possibilities how primal and dual approximated Newton directions can be computed. In particular, it admits the application of both the first- and the second-order methods in this context. The convergence of the method is established. A prototype implementation is discussed and encouraging preliminary computational results are reported for solving the SDP-reformulation of matrix-completion problems.

scholarly journals Local Minima and Convergence in Low-Rank Semidefinite Programming

2004 ◽  
Vol 103 (3) ◽  
pp. 427-444 ◽  
Author(s):  
Samuel Burer ◽  
Renato D.C. Monteiro
Keyword(s):  
Semidefinite Programming ◽  
Low Rank ◽  
Local Minima
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