A potential reduction method for tensor complementarity problems

Abstract

As an extension of linear complementary problem, tensor complementary problem has been effectively applied in n-person noncooperative game. And a multitude of researchers have focused on its properties and theories, while the valid algorithms for tensor complementary problem is still deficient. In this paper, stimulated by the potential reduction method for linear complementarity problem, we present a new algorithm for the tensor complementarity problem, which combines the idea of damped Newton method and the interior point method. Utilizing the new algorithm, we settle the tensor complementary problem with the underlying tensor being diagonalizable and positive definite. Furthermore, the global convergence of the iterative scheme is theoretically guaranteed and the given preliminary numerical experiments indicate the efficiency of the method.

An SDP Method for Copositivity of Partially Symmetric Tensors

“…Particularly, if m � n and x � y, then it reduces to the copositivity of symmetric tensors [1][2][3][4][5][6][7][8][9][10].…”

A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem

“…which is applied to intensity-modulated radiation therapy [1][2][3][4][5][6][7][8][9][10][11], signal processing [12][13][14][15][16][17][18][19][20][21], and image reconstruction [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Censor et al [39] proposed the proximity function pðxÞ to measure the distance of a point to all sets…”

Solvability of Two Classes of Tensor Complementarity Problems

“…In recent several years, the TCP( , A) has been a hot topic and many theoretical results have been obtained, including the nonemptiness and/or compactness of solution set [4][5][6][7][8][9][10][11][12][13][14][15][16], the existence of unique solution [7,8,14,[17][18][19][20][21][22], error bound theory [23][24][25], strict feasibility [22,26], and so on. Several algorithms for solving the TCP( , A) have also been proposed [27][28][29][30][31]. Recently, Wang, Hu, and Huang [14] investigated the quadratic complementarity problem, i.e., find an ∈ R such that ≥ 0,…”