Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide variety of geometric situations, including, for example, Lagrangian plurisubhamonicity and convexity. It also applies in a number of non-geometric situations....

This paper gives a comprehensive analysis of the inverse problem of Lagrangian dynamics for the geodesic equations of the canonical linear connection on Lie groups of dimension four. Starting from the Lie algebra, in every case a faithful four-dimensional representation of the algebra is given as well as one in terms of vector fields and a representation of the linear group of which the given a...

We consider the global and local convergence properties of a class of Lagrangian barrier methods for solving nonlinear programming problems. In such methods, simple bound constraints may be treated separately from more general constraints. The objective and general constraint functions are combined in a Lagrangian barrier function. A sequence of Lagrangian barrier functions are approximately mi...

Solution oscillations, often caused by identical solutions to the homogeneous subproblems, constitute a severe and inherent disadvantage in applying Lagrangian relaxation based methods to resource scheduling problems with discrete decision variables. In this paper, the solution oscillations caused by homogeneous subproblems in the Lagrangian relaxation framework are identified and analyzed. Bas...

Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization, which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a fami...

1993] proposed to solve nonlinear complementarity problems by seeking the unconstrained global minima of a new merit function which they called implicit Lagrangian. A crucial point in such an approach is to determine conditions which guarantee that every uncon-strained stationary point of the implicit Lagrangian is a global solution, since standard unconstrained minimization techniques are only...

In the study of Tonelli Lagrangian and Hamiltonian systems, a central role in understanding the dynamical and topological properties of the action-minimizing sets (also called Mather and Aubry sets), is played by the so-called Mather’s average action (sometimes referred to as β-function or effective Lagrangian), with particular attention to its differentiability and nondifferentiability propert...

W present a new adaptive reconnection-based arbitrary Lagrangian Eulerian: A-ReALE method. The main elements in a A-ReALE method are: An explicit Lagrangian phase on arbitrary polygonal mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined number of mesh cells, their location and connectivity (it is based on using Voronoi tessellatio...

Composite axisymmetric shells have numerous applications; many researchers have taken advantage of the general shell element or the semi-analytical formulation to analyze these structures. The present study is devoted to the nonlinear analysis of composite axisymmetric shells by using a 1D three nodded axisymmetric shell element. Both low and higher-order shear deformations are included in the ...