Optimization Seminar
Thursday, September 15, 2016 · 10:30 - 11:30 AM
This week's talk is the continuation of that from last week!
Title: Polynomial complementarity problems
Speaker: M. Seetharama Gowda
Abstract:
A polynomial complementarity problem is a nonlinear complementarity problem corresponding to a polynomial map on R^n. If the polynomial map is homogeneous, the problem becomes a tensor complementarity problem. (The topic of tensor complementarity problems has become a hot research area within optimization and linear algebra.) In this talk, we describe results connecting the polynomial complementarity problem PCP(f,q) and the tensor complementarity problem PCP(finfty,0), where q is a vector and finfty is the leading term in the decomposition of f as a sum of homogeneous polynomial maps. We show, for example, that PCP(f,q) has a nonempty compact solution set for every q when zero is the only solution of PCP(finfty,0) and the local (topological) degree of min{x,finfty(x)} at the origin is nonzero. Karamardian type results follow from this result. We specialize our results to homogeneous polynomial maps and strengthen/improve many existing results on tensor complementarity problems. We illustrate our results by constructing matrix based tensors.
Title: Polynomial complementarity problems
Speaker: M. Seetharama Gowda
Abstract:
A polynomial complementarity problem is a nonlinear complementarity problem corresponding to a polynomial map on R^n. If the polynomial map is homogeneous, the problem becomes a tensor complementarity problem. (The topic of tensor complementarity problems has become a hot research area within optimization and linear algebra.) In this talk, we describe results connecting the polynomial complementarity problem PCP(f,q) and the tensor complementarity problem PCP(finfty,0), where q is a vector and finfty is the leading term in the decomposition of f as a sum of homogeneous polynomial maps. We show, for example, that PCP(f,q) has a nonempty compact solution set for every q when zero is the only solution of PCP(finfty,0) and the local (topological) degree of min{x,finfty(x)} at the origin is nonzero. Karamardian type results follow from this result. We specialize our results to homogeneous polynomial maps and strengthen/improve many existing results on tensor complementarity problems. We illustrate our results by constructing matrix based tensors.
