We study Lipschitz continuity with respect to the parameter of the set of solutions of a parameterized minimax problem on a product Banach space. We present a sufficient condition ensuring that the map which to any value of the parameter assigns the set of solutions of the problem (possibly multi-valued, and unbounded) possesses Lipschitz-like property, introduced by J.-P. Aubin.

We consider a class of constrained optimization problems where the objective function is a sum of a smooth function and a nonconvex non-Lipschitz function. Many problems in sparse portfolio selection, edge preserving image restoration and signal processing can be modelled in this form. First we propose the concept of the Karush-Kuhn-Tucker (KKT) stationary condition for the non-Lipschitz proble...

In this paper, we study weighted Lp?q minimization model which comprises non-smooth, nonconvex and non-Lipschitz quasi-norm Lp(0 < p ? 1) Lq(1 q 2) for recovering sparse signals. Based on the restricted isometry property (RIP) condition, obtain exact signal recovery result. We also theoretical bound when measurements are depraved by noises.

Any Lipschitz map $f : M \to N$ between two pointed metric spaces may be extended in a unique way to bounded linear operator $\widehat {f} \mathcal {F}(M) {F}(N)$ their corresponding Lipschitz-free spaces. In this paper, we give necessary and sufficient condition for {f}$ compact terms of conditions on $f$ . This extends result by A. Jiménez-Vargas M. Villegas-Vallecillos the case non-separable...

Interpolating discrete volume data into a continuous form adapts implicit surface techniques for rendering volumetric iso-surfaces. One such algorithm uses the Lipschitz condition to create an octree representation that accelerates volume rendering. Furthermore, only one preprocessing step is needed to create the Lipschitz-octree representation that accelerates rendering of iso-surfaces for any...

We consider the existence and uniqueness of Weighted Pseudo almost automorphic solutions to the non-autonomous semilinear differential equation in a Banach space X : ( ) = ( ) ( ) ( , ( )), ' u t A t u t f t u t t R where ( ), , A t t R generates an exponentially stable evolution family { ( , )} U t s and : f X X R satisfies a Lipschitz condition with respect to the second argument. MSC 2010: 4...

In the paper, we study weak invariance of differential inclusions with non-fixed time impulses under compactness type assumptions. When the right-hand side is one sided Lipschitz an extension of the well known relaxation theorem is proved. In this case also necessary and sufficient condition for strong invariance of upper semi continuous systems are obtained. Some properties of the solution set...

We address the problem of designing an observer for triangular non locally Lipschitz dynamical systems. We show the convergence with an arbitrary small error of the classical high gain observer in presence of nonlinearities verifying some Hölder-like condition. Also, for the case when this Hölder condition is not verified, we propose a novel cascaded high gain observer. Under slightly more rest...

In this work, we study the existence of mild solutions and strict solutions of semilinear functional evolution equations with nonlocal conditions, where the linear part is non-autonomous and generates a linear evolution system. The fraction power theory and α-norm are used to discuss the problems so that the obtained results can be applied to the equations in which the nonlinear terms involve s...

In this work we study a class of Secant-like iterations for solving nonlinear and non-differentiable equations in Banach spaces. We consider a condition for divided differences which generalizes those usual ones, i.e, Lipschitz continuous and Hölder continuous conditions. A semilocal convergence result is obtained. For that, we use a technique based on a new system of recurrence relations to ob...