We consider the conic linear program given by a closed convex cone in an Euclidean space and matrix, where vector on right-hand side of inequality constraint defining objective function are subject to change. Using strict feasibility condition, we prove locally Lipschitz continuity obtain some differentiability properties optimal value problem under right-hand-side perturbations. For perturbati...

We study the relationships between Gateaux, Weak Hadamard and Fréchet differentiability and their bornologies for Lipschitz and for convex functions. AMS Subject Classification. Primary: 46A17, 46G05, 58C20. Secondary: 46B20.

The paper deals with investigating approximation abilities of a special class of discrete-time dynamic neural networks. The networks considered are called locally recurrent globally feed-forward, because they are designed with dynamic neuron models which contain inner feedbacks, but interconnections between neurons are strict feed-forward ones like in the well-known multi-layer perceptron. The ...

This paper deals with the analytical and numerical design of a Lyapunov function for homogeneous discontinuous systems. First, presented converse theorems provide two analytic expressions locally Lipschitz continuous functions systems negative homogeneity degree, generalizing classical results. Second, methodology construction those is extended to class under consideration. Finally, developed t...

The minimum time function T (·) of smooth control systems is known to be locally semiconcave provided Petrov’s controllability condition is satisfied. Moreover, such a regularity holds up to the boundary of the target under an inner ball assumption. We generalize this analysis to differential inclusions, replacing the above hypotheses with the continuity of T (·) near the target, and an inner b...

We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range of applications in data science, where the objective is used for inducing sparsity in the solutions while the constraint set models the noise tolerance and ...

Let x 0 be a locally optimal solution of a smooth parametric nonlinear optimization problem minff(x; y) : g(x; y) 0; h(x; y) = 0g for a xed value y = y 0. If the strong suucient optimality condition of second order together with the Mangasarian-Fromowitz and the constant rank constraint qualiications are satissed, then x 0 is strongly stable in the sense of Kojima and the corresponding function...

This paper studies the global output convergence of a class of recurrent neural networks with globally Lipschitz continuous and monotone nondecreasing activation functions and locally Lipschitz continuous time-varying inputs. We establish two sufficient conditions for global output convergence of this class of neural networks. Symmetry in the connection weight matrix is not required in the pres...

We consider a Dirichlet problem for the mean curvature operator in Minkowski spacetime, obtaining necessary and sufficient condition existence of spacelike solution, with prescribed curvature, which is graph function defined on domain equal to complement $\mathbb R^n$ union finite number bounded Lipschitz domains. The $H=H(x,t)$ assumed have absolute value controlled from above by locally bound...

In this paper we describe the notion of a weak lipschitzianity of a mapping on a C stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the Verdier condition.