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06 第四届中国运筹青年论坛 | 青年报告

New Methods for Tensor Complementarity Problems

杜守强 青岛大学

This report is concerned with the tensor complementarity problems. We consider the new methods

for solving the tensor complementarity problems. The tensor complementarity problems also include
stochastic structured tensor complementarity problems and tensor eigenvalue complementarity
problems. We propose the mixed integer method to solve the tensor complementarity problem by
equivalent mixed integer programming formulations. Furthermore, the bounded of the solution set is

proved with some kinds of tensor complementarity problems. The stochastic structured tensor
complementarity problems are also considered. A projected gradient method is proposed to solve the
stochastic structured tensor complementarity problems. Finally, we consider the new methods for
tensor eigenvalue complementarity problems.

Solution to a Problem of Godsil Regarding

Inverses of Bipartite Graphs

杨玉军 烟台大学

In this talk, we provide a characterization of bipartite graphs with unique perfect matchings such

that the inverses of their adjacency matrices are diagonally similar to non-negative matrices, which

settles an open problem of Godsil on inverses of bipartite graphs with unique perfect matchings in

[Godsil, Inverses of Trees, Combinatorica 5 (1985) 33-39].