This paper will review recent advances in the formulation of a discrete version of geometric mechanics, based on the discretization of Hamilton’s variational principle, and progress that has been made in reduction theory for discrete variational mechanics in the form of Discrete Routh Reduction. To place discrete geometric mechanics on a firm mathematical foundation, we propose to develop a dis...

The paper continues the discussion of continuum theory of dislocations suggested by Berdichevsky and Sedov (PMM 31(6): 981–1000, 1967). The major new points are: the choice of energy, the variational form of the governing dynamical equations, the variational principle for the final plastic state.

This work is concerned with the analysis of convergence properties of feasible descent methods for solving monotone variational inequalities in Banach spaces.

In this paper directionally contextual concepts of variational analysis, based on dual-~pace cou-siructions similar to those in [4, 5], are introduced and studied. As an illustration of their usefulnes~, necessary and ft!so sufficient optimality conditions in terms of directioual subdiffeJ • ent.ials are established , and it is shown that they can be effective in the situations where known opti...

We present some error bound results of generalized D-gap functions for nonsmooth and nonmonotone variational inequality (VI) problems. Application is given in providing a derivative-free descent method.

In this paper, we give several existence theorems for solutions of the generalized quasi–variational inequalities under new conditions. Even in topological vector spaces, our results are new.

Using variational analysis, we study the linear regularity for a collection of finitely many closed sets. In particular, we extend duality characterizations of the linear regularity for a collection of finitely many closed convex sets to the possibly nonconvex setting. Moreover the sharpest linear regularity constant can also be dually represented under the subsmoothness assumption.

We prove the existence of solutions to systems of degenerate variational inequalities. In this note we give a short proof of the following Theorem obtained in [1] not relying on the partial regularity theory.

We consider a generalized ε-vector equilibrium problem which contain vector equilibrium problems and vector variational inequalities as special cases. By using the KKM theorem,we obtain some existence theorems for the generalized ε-vector equilibrium problem. We also investigate the duality of this generalized ε-vector equilibrium problem and discuss the equivalence relation between solutions o...