We study discrete-time quantum walks on $d$-cycles with a position and coin-dependent phase-shift. Such model simulates dynamics of particle moving ring an artificial gauge field. In our case the amplitude phase-shift is governed by single discrete parameter $q$. solve analytically observe that for prime $d$ there exists strong complementarity property between eigenvectors two walk evolution op...

In this paper a branch-and-bound algorithm is proposed for finding a global minimum to a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPECs), which incorporates disjunctive cuts for computing lower bounds and employs a Complementarity Active-Set Algorithm for computing upper bounds. Computational results for solving MPECs associated with Bilivel Problems, ...

In this paper, we first give a new equivalent optimization form to nonlinear complementarity problems and then establish a damped Newton method in which penalty technique is used. The subproblems of the method are lower-dimensional linear complementarity problems. We prove that the algorithm converges globally for strongly monotone complementarity problems. Under certain conditions, the method ...

Regularization methods for the solution of nonlinear complementarity problems are standard methods for the solution of monotone complementarity problems and possess strong convergence properties. In this paper, we replace the monotonicity assumption by a P0-function condition. We show that many properties of regularization methods still hold for this larger class of problems. However, we also p...

In this paper, We introduce a new class of generalized vector complementarity problems and the corresponding generalized vector variational inequality problems which include many known complementarity problems and the corresponding vector variational inequality problems as special cases and establish the equivalence between those problems in Banach spaces. Furthermore, we obtain some new existe...