For an implicit multifunction (p) defined by the generally nonsmooth equation F(x, p) = 0, contingent derivative formulas are derived, being similar to the formula ′ = −Fx−1Fp in the standard implicit function theorem for smooth F and . This will be applied to the projection X(p) = {x | ∃y: (x, y) ∈ (p)} of the solution set (p) of the system F(x, y, p) = 0 onto the x-space. In particular settin...

The authors prove existence of a stable transfer function satisfying the nonlinear equations characterizing an asymptotic stationary point, in undermodeled cases, for a class of pseudo-linear regression algorithms, including Landau’s algorithm, the Feintuch algorithm, and (S)HARF. The proof applies to all degrees of undermodeling and assumes only that the input power spectral density function i...

H. Kröger, G. Melkonyan, F. Paradis, S.G. Rubin a Département de Physique, Université Laval, Québec, Québec G1K 7P4, Canada b Moscow State Engineering Physics Institute, Kashirskoe sh., 31, Moscow 115409, Russia c Center for Cosmoparticle Physics ”Cosmion”, Moscow, 125147, Russia Abstract We investigate the dynamics of gravity coupled to a scalar field using a non-canonical form of the kinetic ...

In the recent paper [3], it was shown that the stochastic subgradient method applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate O(k−1/4). In this supplementary note, we present a stochastic subgradient method for minimizing a convex function, with the improved rate Õ(k−1/2).

P-fuzzy dynamical systems are variational systems whose dynamic is obtained by means of a Mamdani type fuzzy rule-based system. In this paper, particularly, we are going to approach the 1-dimensional p-fuzzy dynamical systems and will present theorems that establish conditions of existence and uniqueness of stationary points. Besides the obtained analytical results, we will present examples tha...

Mathematical program with equilibrium constraints (MPEC) has extensive applications in practical areas such as traffic control, engineering design, and economic modeling. Some generalized stationary points of MPEC are studied to better describe the limiting points produced by interior point methods for MPEC. A primal-dual interior point method is then proposed, which solves a sequence of relaxe...

In this talk we characterize the transonic stationary solutions of the hydrodynamic escape problem (HEP), which is significant on studying the evolution of atmospheres of planets. The characterization is established by the geometric singular perturbation method (GSP) on the wind solution of HEP. We will discuss the existence and non-existence of the adiabatic wind solution with or without heat ...

While its performance in the Gaussian, infinite block length, and loopless factor graph cases are well understood, the breakthrough applications of the belief propagation algorithm to the decoding of turbo and LDPC codes involve finite block lengths, finite alphabets, and factor graphs with loops. It has been shown in these instances that the stationary points of the belief propagation decoder ...

Augmented Lagrangian methods with convergence to second-order stationary points in which any constraint can be penalized or carried out to the subproblems are considered in this work. The resolution of each subproblem can be done by any numerical algorithm able to return approximate second-order stationary points. The developed global convergence theory is stronger than the ones known for curre...