抄録
Sequences of generalized Lagrangian duals and their sums of squares (SOS) of polynomials relaxations for a polynomial optimization problem (POP) are introduced. The 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 approach. The sequence of SOS relaxations is transformed into a sequence of semidefinite programing (SDP) relaxations of the POP, which correspond to duals of modification and generalization of SDP relaxations given by Lasserre for the POP.
本文言語 | 英語 |
---|---|
ページ(範囲) | 697-719 |
ページ数 | 23 |
ジャーナル | SIAM Journal on Optimization |
巻 | 15 |
号 | 3 |
DOI | |
出版ステータス | 出版済み - 2005 |
外部発表 | はい |
!!!All Science Journal Classification (ASJC) codes
- ソフトウェア
- 理論的コンピュータサイエンス