In this thesis we investigate nonsmooth classical and continuum mechanics and its discretizations by means of variational numerical and geometric methods. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Next, we develop the f...

In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

Limit cycles are common in hybrid systems. However the nonsmooth dynamics of such systems makes stability analysis difficult. This paper uses recent extensions of trajectory sensitivity analysis to obtain the characteristic multipliers of nonsmooth limit cycles. The stability of a limit cycle is determined by its characteristic multipliers. The concepts are illustrated using a coupled tank syst...

A basic relationship is derived between generalized subgradients of a given function, possibly nonsmooth and nonconvex, and those of a second function obtained from it by partial conjugation. Applications are made to the study of multiplier rules in finite-dimensional optimization and to the theory of the Euler-Lagrange condition and Hamiltonian condition in nonsmooth optimal control.

Proximity control is a well-known mechanism in bundle method for nonsmooth optimization. Here we show that it can be used to optimize a large class of nonconvex and nonsmooth functions with additional structure. This includes for instance nonconvex maximum eigenvalue functions, and also infinite suprema of such functions.

The existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous Neumann boundary conditions. Using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous Neumann boundary conditions, we obtain the result.

For a nonsmooth multiobjective mathematical programming problem governed by infinitely many constraints‎, ‎we define a new gap function that generalizes the definitions of this concept in other articles‎. ‎Then‎, ‎we characterize the efficient‎, ‎weakly efficient‎, ‎and properly efficient solutions of the problem utilizing this new gap function‎. ‎Our results are based on $(Phi,rho)-$invexity‎,...

Error modelling has played a major role in generating post-corrections of analogue to digital converters (ADC). Benefits by using parametric models for post-correction are that they requires less memory and that they are easier to identify for arbitrary signals. However, the parameters are estimated in two steps; firstly, the integral nonlinearity (INL) is estimated and secondly, the model para...

This paper presents a nonsmooth optimization technique for solving a special μsynthesis control problem. Attention is focused on controller synthesis problems that involve real diagonal scalings. An academic example illustrates the synthesis algorithm and a comparison is made with the well-known DK-iteration algorithm. This paper shows that nonsmooth optimization synthesis can provide better so...