Abstract
In this paper, we study the sparse solution of the tensor complementarity problem (TCP), which is an NP hard problem due to the nonconvexity and noncontinuity of the ℓ0 norm. We transform the complementarity constraints into a fixed point equation with projection type and use 0/1-loss function to relax ℓ0 norm. We develop a smoothing Newton projection (SNP) algorithm to solve the transformed problem. The subproblem with 0/1-loss function is solved by Newton method. Finally, numerical results show that the SNP algorithm can effectively get the sparse solution to a TCP.
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