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Properties of a class of nonlinear transformations over Euclidean Jordan algebras with applications to complementarity problems. (English) Zbl 1180.90340

The authors first consider properties of the so-called relaxation transformations in a Euclidean Jordan algebra, which are based on the Pierce decomposition. Namely, they establish that it maintains Lipschitz continuity, differentiability, monotonicity and some related properties. Next, they propose a smoothing Newton algorithm for a symmetric cone complementarity problem associated with the transformation mapping and establish its convergence under monotonicity assumptions.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
17C55 Finite-dimensional structures of Jordan algebras
17C27 Idempotents, Peirce decompositions

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[1] DOI: 10.1016/j.laa.2004.03.028 · Zbl 1072.15002
[2] Kong L.C., Math. Oper. Res. (2007)
[3] DOI: 10.1007/s11590-006-0037-y · Zbl 1220.90133
[4] Lin Y., A Homogeneous Model for Mixed Complementarity Problems over Symmetric Cones (2005)
[5] DOI: 10.1142/S0217595906000991 · Zbl 1202.90252
[6] DOI: 10.1287/moor.1070.0300 · Zbl 1218.90197
[7] DOI: 10.1287/moor.1050.0157 · Zbl 1278.90408
[8] DOI: 10.1137/04061427X · Zbl 1136.90039
[9] DOI: 10.1023/A:1009701824047 · Zbl 0973.90095
[10] DOI: 10.1016/S0377-0427(97)00153-2 · Zbl 0889.65066
[11] DOI: 10.1007/s10107-003-0424-4 · Zbl 1035.90099
[12] DOI: 10.1007/s11425-008-0170-4 · Zbl 1203.90123
[13] Huang Z.H., Comput. Optim. Appl. (2008)
[14] DOI: 10.1137/060676775 · Zbl 1182.65092
[15] Lu Y., SIAM J. Optim. 18 pp 65– (2007)
[16] DOI: 10.1016/j.jmaa.2009.01.064 · Zbl 1180.90341
[17] DOI: 10.1287/moor.26.3.543.10582 · Zbl 1073.90572
[18] DOI: 10.1007/s10107-003-0380-z · Zbl 1023.90083
[19] Faraut U., Analysis on Symmetric Cones (1994) · Zbl 0841.43002
[20] DOI: 10.1007/BF01455996 · Zbl 0552.17014
[21] Gowda M.S., Semidefinite Relaxations of Linear Complementarity Problems (2002)
[22] DOI: 10.1137/S1052623400380584 · Zbl 1076.90042
[23] Clarke F.H., Optimization and Nonsmooth Analysis (1983) · Zbl 0582.49001
[24] DOI: 10.1287/moor.1050.0182 · Zbl 1168.90620
[25] Luc D.T., J. Convex Anal. 3 pp 195– (1996)
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