In this paper, we investigate the semismooth Newton and quasi-Newton methods for the minimization problem in the weighted `−regularization of nonlinear inverse problems. We propose the conditions for obtaining the convergence of two methods. The semismooth Newton method is proven to locally converge with superlinear rate and the semismooth quasi-Newton method is proven to locally converge at le...

We study the local convergence of a predictor-corrector algorithm for semideenite programming problems based on the Monteiro-Zhang uniied direction whose polynomial convergence was recently established by Monteiro. We prove that the suucient condition for superlinear convergence of Potra and Sheng applies to this algorithm and is independent of the scaling matrices. Under strict complementarity...

We propose and analyze a perturbed version of the classical Josephy-Newton method for solving generalized equations. This perturbed framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilzed version, sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods. For the linearly constrained Lagrangian meth...

In this paper, we present a detailed investigation for the properties of a oneparametric class of SOC complementarity functions, which include the globally Lipschitz continuity, strong semismoothness, and the characterization of the B-subdifferential at a general point. Moreover, for the merit functions induced by them for the second-order cone complementarity problem (SOCCP), we provide a cond...

In this paper, we will establish some new oscillation criteria for the second-order superlinear neutral delay dynamic equation of Emden-Fowler type [ a(t)(y(t) + r(t)y(τ(t))) ]∆ + p(t) |y(δ(t))| signy(δ(t)) = 0, on a time scale T; here γ > 1, a(t), r(t), τ(t), p(t) and δ(t)real-valued positive functions defined on T. Our results in the special case when T = R, improve the oscillation results fo...

A swarm-bot is a robotic entity built of several autonomous mobile robots (called s-bots) physically connected together. This form of collective robotics exploits robot interactions both at the behavioral and physical levels. The goal of this paper is to analyze the physical performance of a swarm-bot as function of its size (number n of s-bots composing it). We present three tasks and the corr...

We study perturbations of the eigenvalue problem for the negative Laplacian plus an indefinite and unbounded potential and Robin boundary condition. First we consider the case of a sublinear perturbation and then of a superlinear perturbation. For the first case we show that for λ < λ̂1 (λ̂1 being the principal eigenvalue) there is one positive solution which is unique under additional conditions...

In this paper, we study the existence and stability of travelling wave solutions of a kinetic reactiontransport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction term of monostable type. The boundedness of the velocity set appears to be a necessary and sufficient condition for the existence of positive travelling waves. T...

Let H : <m×<n → <n be a locally Lipschitz function in a neighborhood of (ȳ, x̄) and H(ȳ, x̄) = 0 for ȳ ∈ <m and x̄ ∈ <n. The implicit function theorem in the sense of Clarke [1, 2] says that if πx∂H(ȳ, x̄) is of maximal rank, then there exist a neighborhood Y of ȳ and a Lipschitz function G(·) : Y → <n such that G(ȳ) = x̄ and for every y in Y , H(y,G(y)) = 0. In this paper, we shall further show tha...

We present a generalized Newton method and a quasiNewton method for solving H(x) := F(nc(x))+x-nc(x) = 0, when C is a polyhedral set. For both the Newton and quasi-Newton methods considered here, the subproblem to be solved is a linear system of equations per iteration. The other characteristics of the quasi-Newton method include: (i) a g-superlinear convergence theorem is established without a...