This work develops robust contact algorithms capable of dealing with complex contact situations involving several bodies with corners. Amongst the mathematical tools we bring to bear on the problem is nonsmooth analysis, following [14]. We speci cally address contact geometries for which both the use of normals and gap functions have difculties and therefore precludes the application of most co...

In this paper we present conditions ensuring the existence and localization of lower and upper functions of the periodic boundary value problem u + k u = f(t, u), u(0) = u(2 ), u(0) = u(2 ), k ∈ , k 6= 0. These functions are constructed as solutions of some related generalized linear problems and can be nonsmooth in general.

For a class of nonconvex nonsmooth functions, we consider the problem of computing an approximate critical point, in the case when only inexact information about the function and subgradient values is available. We assume that the errors in function and subgradient evaluations are merely bounded, and in principle need not vanish in the limit. We examine the redistributed proximal bundle approac...

In this paper we develop a stability theory for broad classes of parametric generalized equations and variational inequalities in finite dimensions. These objects have a wide range of applications in optimization, nonlinear analysis, mathematical economics, etc. Our main concern is Lipschitzian stability of multivalued solution maps depending on parameters. We employ a new approach of nonsmooth...

In the paper, we obtain new sufficient conditions ensuring existence, uniqueness, and asymptotic stability of the equilibrium point for delayed neural network via nonsmooth analysis, which makes use of the Lipschitz property of the functions. Based on this tool of nonsmooth analysis, we first obtain a couple of general results concerning the existence and uniqueness of the equilibrium point. Th...

An extension of a new multidimensional bisection method for minimizing function over simplex is proposed for solving nonlinear unconstrained minimization problem. The method does not require a differentiability of function, and is guaranteed to converge to the minimizer for the class of strictly unimodal functions. The computational results demonstrating an effectiveness of algorithm for minimi...

Variational analysis concerns the geometry and calculus of nonsmooth sets and functions, often viewed from an optimization perspective. Over several decades, variational analysis has matured into a powerful and elegant theory. One rich source of concrete examples involves the eigenvalues of symmetric and nonsymmetric matrices, sometimes deriving from dynamical or feedback control questions. Thi...

Many real-world optimization models comprise nonconvex and nonlinear as well as nonsmooth functions leading to very hard classes of optimization models. In this article a new interior-point method for the special but practically relevant class of optimization problems with locatable and separable nonsmooth aspects is presented. After motivating and formalizing the problems under consideration, ...

An efficient Particle Swarm Optimization (PSO) technique, employed to solve Economic Dispatch (ED) problems in power system is presented in this paper. With practical consideration, ED will have nonsmooth cost functions with equality and inequality constraints that makes the problem, a large-scale highly constrained nonlinear optimization problem.The proposed method expands the original PSO to ...

The paper concerns first-order necessary optimality conditions for problems of minimizing nonsmooth functions under various constraints in infinite-dimensional spaces. Based on advanced tools of variational analysis and generalized differential calculus, we derive general results of two independent types called lower subdifferential and upper subdifferential optimality conditions. The former on...