It is highly desirable for numerical approximations to stationary points for a potential energy landscape to lie in the corresponding quadratic convergence basin. However, it is possible that an approximation may lie only in the linear convergence basin, or even in a chaotic region, and hence not converge to the actual stationary point when further optimization is attempted. Proving that a nume...

It is well known that an upper semi-continuous compactand convex-valued mapping φ from a nonempty compact and convex set X to the Euclidean space of which X is a subset has at least one stationary point, being a point in X at which the image φ(x) has a nonempty intersection with the normal cone at x. In many circumstances there may be more than one stationary point. In this paper we refine the ...

Computing the epipolar geometry between cameras with very different viewpoints is often very difficult. The appearance of objects can vary greatly, and it is difficult to find corresponding feature points. Prior methods searched for corresponding epipolar lines using points on the convex hull of the silhouette of a single moving object. These methods fail when the scene includes multiple moving...

We present a new relaxation scheme for mathematical programs with equilibrium constraints (MPEC), where the complementarity constraints are replaced by a reformulation that is exact for the complementarity conditions corresponding to sufficiently non-degenerate complementarity components and relaxes only the remaining complementarity conditions. A positive parameter determines to what extent th...

In this paper, optimality conditions for the group sparse constrained optimization (GSCO) problems are studied. Firstly, equivalent characterizations of Bouligand tangent cone, Clarke cone and their corresponding normal cones set derived. Secondly, by using cones, four types stationary points GSCO given: TB-stationary point, NB-stationary TC-stationary point NC-stationary which used to characte...

The first law of black hole mechanics was derived by Wald in a general covariant theory of gravity for stationary variations about a stationary black hole. Although it has many advantages, there are several ambiguous points in the derivation. In this paper we point out them and give a clearer derivation of it. After that, we show that there remains a problem when we consider non-stationary pert...

We take a new look to adaptive IIR lattice filters in order to devise algorithms that preserve the stability of the corresponding direct form schemes. By analizing the local properties of stationary points, a transformation achieving this goal is suggested, which gives algorithms that can be efficiently implemented. Application to the Steiglitz-McBride and SHARF algorithms is presented. By cont...