Abstract
A novel primal-dual path-following interior-point algorithm for the Cartesian P*(k)-linear complementarity problem over symmetric cones is presented. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov-Todd step feasible interior-point algorithm based on the new search directions, the complexity bound of the algorithm with small-update approach is the best-available bound.
Highlights
The SCLCP includes a wide class of problems, namely, linear complementarity problem (LCP), second-order cone linear complementarity problem (SOCLCP) and semidefinite linear complementarity problem (SDLCP) as special cases
For a comprehensive study on recent developments related to symmetric cone complementarity problems (SCCP), the reader is referred to [20]
In developing the results it is assumed that the Cartesian P∗(κ)-SCLCP satisfies the interior-point condition (IPC), i.e., there exists x0, s0 ∈ intK such that s0 = A(x0) + q [10]
Summary
Let (J , ◦) be the Cartesian product of a finite number of Euclidean Jordan algebras, i.e.,. J = J1 × J2 × · · · × JN , with its cone of squares K = K1 × K2 × · · · × KN , where Jj is an nj-dimensional Euclidean Jordan algebra with n =. A : J → J and a q ∈ J , the linear complementarity problem over symmetric cones (SCLCP) is to find x, s ∈ J such that x ∈ K, s = A(x) + q ∈ K, and x, s = 0, where x, s , denotes the Euclidean inner product. The SCLCP includes a wide class of problems, namely, linear complementarity problem (LCP), second-order cone linear complementarity problem (SOCLCP) and semidefinite linear complementarity problem (SDLCP) as special cases.
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