Recently, the problem of local minima in very high dimensional non-convex optimization has been challenged and the problem of saddle points has been introduced. This paper introduces a dynamic type of normalization that forces the system to escape saddle points. Unlike other saddle point escaping algorithms, second order information is not utilized, and the system can be trained with an arbitra...

In this paper, we study the existence of local and global saddle points for nonlinear second-order cone programming problems. The existence of local saddle points is developed by using the second-order sufficient conditions, in which a sigma-term is added to reflect the curvature of second-order cone. Furthermore, by dealing with the perturbation of the primal problem, we establish the existenc...

In this paper, we further investigate the local Hermitian and skew-Hermitian splitting (LHSS) iteration method and the modified LHSS (MLHSS) iteration method for solving generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. When A is non-symmetric positive definite, the convergence conditions are obtained, which generalize some results of Jiang and Cao [M.-Q. Jiang and Y. Ca...

In present-day optical system design, it is tacitly assumed that local minima are points in the merit function landscape without relationships between them. We will show however that there is a certain degree of order in the design landscape and that this order is best observed when we change the dimensionality of the optimization problem and when we consider not only local minima, but saddle p...

This paper presents the design analysis of saddle support of a horizontal pressure vessel. Since saddle have the vital role to support the pressure vessel and to maintain its stability, it should be designed in such a way that it can afford the vessel load and internal pressure of the vessel due to liquid contained in the vessel. A model of horizontal pressure vessel and saddle support is creat...

We compute the full three-dimensional momentum space distribution of ejected electrons resulting from alpha particle impact ionization of hydrogen. At low impact velocities the transverse momentum distributions are shown to exhibit strong oscillations with energy. For the longitudinal component, the momentum distribution peaks near the target at high energies, shifts towards the projectile cent...

In this paper, we prove the existence of a chaotic saddle for a piecewise-linear map of the plane, referred to as the Lozi map. We study the Lozi map in its orientation and area preserving version. First, we consider the autonomous version of the Lozi map to which we apply the Conley–Moser conditions to obtain the proof of a chaotic saddle. Then we generalize the Lozi map on a nonautonomous ver...

We investigate refinements of two solutions, the saddle and the weak saddle, defined by Shapley (1964) for two-player zero-sum games. Applied to weak tournaments, the first refinement, the mixed saddle, is unique and gives us a new solution, generally lying between the GETCHA and GOTCHA sets of Schwartz (1972, 1986). In the absence of ties, all three solutions reduce to the usual top cycle set....

This paper reports on a micro saddle coil for local high-resolution magnetic resonance imaging (MRI) fabricated by embedding a flexible coil pattern into a polydimethyilsiloxane (PDMS) tube. We can change the sensitivity of the micro coil by deforming the shape of the coil from a saddle-shaped mode to a planar-shaped mode. The inductance, the resistance, and the Q-factor of the coil in the sadd...