Abstract
We present a smooth approximation for the generalized Fischer-Burmeister function where the 2-norm in the FB function is relaxed to a general p-norm (p > 1), and establish some favorable properties for it - for example, the Jacobian consistency. With the smoothing function, we transform the mixed complementarity problem (MCP) into solving a sequence of smooth system of equations, and then trace a smooth path generated by the smoothing algorithm proposed by Chen (2000) [28] to the solution set. In particular, we investigate the influence of p on the numerical performance of the algorithm by solving all MCPLIP test problems, and conclude that the smoothing algorithm with p ∈ (1, 2] has better numerical performance than the one with p > 2.
| Original language | English |
|---|---|
| Pages (from-to) | 3739-3758 |
| Number of pages | 20 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 72 |
| Issue number | 9-10 |
| DOIs | |
| Publication status | Published - 2010 May 1 |
Keywords
- Convergence rate
- Mixed complementarity problem
- Smoothing approximation
- The generalized FB function
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
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Chen, J-S., Pan, S., & Lin, T. C. (2010). A smoothing Newton method based on the generalized Fischer-Burmeister function for MCPs. Nonlinear Analysis, Theory, Methods and Applications, 72(9-10), 3739-3758. https://doi.org/10.1016/j.na.2010.01.012