期刊
JOURNAL OF GLOBAL OPTIMIZATION
卷 52, 期 3, 页码 447-469出版社
SPRINGER
DOI: 10.1007/s10898-011-9757-3
关键词
Reformulation-Linearization Technique (RLT); Reduced basis techniques; Polynomial programs; Global optimization; Semidefinite cuts; BARON
资金
- National Science Foundation [CMMI-0969169]
- [ANR 07-JCJC-0151]
- [2009-14D]
- [2009-55D]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [0969169] Funding Source: National Science Foundation
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [0968909] Funding Source: National Science Foundation
This paper explores equivalent, reduced size Reformulation-Linearization Technique (RLT)-based formulations for polynomial programming problems. Utilizing a basis partitioning scheme for an embedded linear equality subsystem, we show that a strict subset of RLT defining equalities imply the remaining ones. Applying this result, we derive significantly reduced RLT representations and develop certain coherent associated branching rules that assure convergence to a global optimum, along with static as well as dynamic basis selection strategies to implement the proposed procedure. In addition, we enhance the RLT relaxations with v-semidefinite cuts, which are empirically shown to further improve the relative performance of the reduced RLT method over the usual RLT approach. We present computational results for randomly generated instances to test the different proposed reduction strategies and to demonstrate the improvement in overall computational effort when such reduced RLT mechanisms are employed.
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