Chen, Xin; Tseng, Paul Non-interior continuation methods for solving semidefinite complementarity problems. (English) Zbl 1023.90046 Math. Program. 95, No. 3 (A), 431-474 (2003). Summary: There recently has been much interest in non-interior continuation/smoothing methods for solving linear/nonlinear complementarity problems. We describe extensions of such methods to complementarity problems defined over the cone of block-diagonal symmetric positive semidefinite real matrices. These extensions involve the Chen-Mangasarian class of smoothing functions and the smoothed Fischer-Burmeister function. Issues such as existence of Newton directions, boundedness of iterates, global convergence, and local superlinear convergence will be studied. Preliminary numerical experience on semidefinite linear programs is also reported. Cited in 3 ReviewsCited in 66 Documents MSC: 90C22 Semidefinite programming 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) Keywords:semidefinite complementarity problem; smoothing function; non-interior continuation; global convergence; local superliner convergence Software:SDPT3 PDFBibTeX XMLCite \textit{X. Chen} and \textit{P. Tseng}, Math. Program. 95, No. 3 (A), 431--474 (2003; Zbl 1023.90046) Full Text: DOI