The aim of the session is to present state-of-the-art and current research directions in variational analysis and in applications to equilibrium problems. Variational analysis encompasses a large area of modern mathematics, including the classical calculus of variations, the theories of perturbation, approximation, subgradient, set convergence, variational inequalities and partial di↵erential e...

Fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. For that reason, we need a reliable and efficient technique for the solution of fractional differential equations. The aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

We will discuss some new results for the inverse problem of Variational Calculus. We will consider problems with functionals given by action forms of order greater than one and subject to non-holonomic constraints.

We discuss intrinsic aspects of Krupka’s approach to finite–order variational sequences. We give intrinsic isomorphisms of the quotient subsheaves of the short finite– order variational sequence with sheaves of forms on jet spaces of suitable order, obtaining a new finite–order (short exact) variational sequence which is made by sheaves of polynomial differential operators. Moreover, we present...

Geometric structure of global integral variational functionals on higher order tangent bundles and Grassmann fibrations are investigated. The theory of Lepage forms is extended to these structures. The concept of a Lepage form allows us to introduce the Euler-Lagrange distribution for variational functionals, depending on velocities, in a similar way as in the calculus of variations on fibred m...

This paper presents, an efficient approach for solving Euler-Lagrange Equation which arises from calculus of variations. Homotopy analysis method to find an approximate solution of variational problems is proposed. An optimal value of the convergence control parameter is given through the square residual error. By minimizing the square residual error, the optimal convergence-control parameters ...

The calculus of variations is an important tool in the study of boundary value problems for differential systems. A development of this approach, called the control variational method, is based on the use of the optimal control theory, especially of the Pontryagin maximum principle. In this presentation, we review the results established in the literature on the control variational method and i...

The variational inequality problem provides a broad unifying setting for the study of optimization, equilibrium and related problems and serves as a useful computational framework for the solution of a host of problems in very diverse applications. Variational inequalities have been a classical subject in mathematical physics, particularly in the calculus of variations associated with the minim...

The calculus of variations for lagrangians which are not functions on the tangent bundle, but sections certain affine bundles is developed. We follow a general approach to variational principles which admits boundary terms of variations. MSC 2000: 70G45, 70H03, 70H05

The role of design optimization in CAD is central. Classical theories of optimization (differential calculus, variational calculus, optimal control theory, mathematical programming) deal with the case when this domain design parameters is infinite. From this angle, the subject of discrete optimization, where the domain design parameters is typically finite, might seem trivial : it is easy to sa...