Properties of the Log-Barrier Function on Degenerate Nonlinear Programs

Properties of the Log - Barrier Function on Degenerate

We examine the sequence of local minimizers of the log-barrier function for a non-linear program near a solution at which second-ordersuucient conditionsand the Mangasarian-Fromovitz constraint qualiications are satissed, but the active constraint gradients are not necessarily linearly independent. When a strict complementarity condition is satissed, we show uniqueness of the local minimizer of...

Degenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind

Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...

Quantum current modelling on tri-layer graphene nanoribbons in limit degenerate and non-degenerate

Graphene is determined by a wonderful carrier transport property and high sensitivityat the surface of a single molecule, making them great as resources used in Nano electronic use.TGN is modeled in form of three honeycomb lattices with pairs of in-equivalent sites as {A1, B1},{A2, B2}, and {A3, B3} which are located in the top, center and bottom layers, respectively. Trilayer...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

On the convergence of the Newton/log-barrier method

In the Newton/log-barriermethod,Newton steps are taken for the log-barrier function for a xed value of the barrier parameter until a certain convergence criterion is satis ed. The barrier parameter is then decreased and the Newton process is repeated. A naive analysis indicates that Newton's method does not exhibit superlinear convergence to the minimizer of each instance of the log-barrier fun...