When multiple followers are involved in a bilevel decision problem, the leader’s decision will be affected, not only by the reactions of these followers, but also by the relationships among these followers. One of the popular situations within this framework is where these followers are uncooperatively making decisions while having cross reference of decision information. This situation is call...

Recently, a number of authors have presented several geometries for rankstructured matrix and tensor spaces, namely the set of matrices or tensors with fixed matrix, Tucker or TT rank. In this talk we present a unifying approach for establishing a smooth, differential structure on the set of tensors with fixed hierarchical Tucker rank. Our approach describes this set as a smooth submanifold, gl...

The majority of research on bilevel programming has centered on the linear version of the problem in which only one leader and single follower are involved. This paper proposes a general model and Kuhn-Tucker approach for linear bilevel programming problems in which one leader and multiple follower(s) are involved, and there may (not) be sharing variables among the followers. Finally, a numeric...

This paper is a counterpart of [2]. Specifically, for a locally optimal solution to the nonlinear second-order cone programming (SOCP), under Robinson’s constraint qualification, we establish the equivalence among the following three conditions: the nonsingularity of Clarke’s Jacobian of Fischer-Burmeister (FB) nonsmooth system for the Karush-Kuhn-Tucker conditions, the strong second-order suff...

Vartul Sangal, Leena Nieminen, Barbara Weinhardt, Jane Raeside, Nicholas P. Tucker, Catalina-Diana Florea, Kevin G. Pollock, and Paul A. Hoskisson Author affiliations: Strathclyde Institute of Pharmacy and Biomedical Sciences, University of Strathclyde, Glasgow, Scotland UK (V. Sangal, L. Nieminen, N.P. Tucker, P.A. Hoskisson); Faculty of Health and Life Sciences, Northumbria University, Newcas...