by Sunyoung Kim, Masakazu Kojima, Hayato Waki
SIAM J. Optim
http://www.is.titech.ac.jp/research/research-report/B/B-395.ps.gz
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Abstract:
Sequences of generalized Lagrangian duals and their SOS (sums of squares of polynomials) relaxations for a POP (polynomial optimization problem) are introduced. Sparsity of polynomials in the POP is used to reduce the sizes of the Lagrangian duals and their SOS relaxations. It is proved that the optimal values of the Lagrangian duals in the sequence converge to the optimal value of the POP using a method from the penalty function approaches. The sequence of SOS relaxations is transformed into a sequence of SDP (semidefinite program) relaxations of the POP, which correspond to duals of modification and generalization of SDP relaxations given by Lasserre for the POP. Key words.
Citations
|
157
|
A lift-and-project cutting plane algorithm for mixed 0-1 programs
– Balas, Ceria, et al.
- 1993
|
|
93
|
A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems
– Sherali, Adams
- 1990
|
|
69
|
Semidefinite programming relaxations for semi-algebraic problems
– Parrilo
|
|
50
|
Positive polynomials on compact semi-algebraic sets
– PUTINAR
|
|
26
|
A Global Optimization Algorithm for Polynomial Programming Problems Using a Reformulation-Linearization Technique
– Sherali, Tuncbilek
- 1992
|
|
24
|
Discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization problems
– KOJIMA, TUNC, et al.
- 1998
|
|
22
|
A Hierarchy of Relaxations and Convex Hull Characterizations for Mixed-Integer Zero-One Programming Problems
– Sherali, Adams
- 1994
|
|
17
|
Sums of squares of real polynomials
– Choi, Lam, et al.
- 1995
|
|
15
|
An algorithm for sums of squares of real polynomials
– Powers, Wörmann
- 1998
|
|
13
|
A general framework for convex relaxation of polynomial optimization problems over cones
– Kojima, Kim, et al.
- 2003
|
|
13
|
Sparsity in sums of squares of polynomials
– Kojima, Kim, et al.
- 2005
|
|
13
|
Extremal psd forms with few terms
– Reznick
- 1978
|
|
12
|
second-order methods for semidefinite programming
– Monteiro
- 2003
|
|
11
|
Parrilo, “SOSTOOLS: Sum of Squares Optimization Toolbox for
– Prajna, Papachristodoulou, et al.
- 2002
|
|
9
|
Cones of matrices and set functions and 0-1 optimization
– LovAsz, Schrijver
- 1991
|
|
8
|
Second order cone programming relaxation of nonconvex quadratic optimization problems
– Kim, Kojima
- 2001
|
|
6
|
Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP relaxations
– Kim, Kojima
- 2002
|
|
3
|
Lasserre: Global optimization with polynomials and the problems of moments
– B
|
|
2
|
and Levent Tuncel, Cones of Matrices and Successive Convex Relaxations of Nonconvex Sets
– Kojima
- 2000
|
