Abstract Lagrangian models use calculus to solve multi-variable non-linear constrained optimization of problems and for identifying the marginal changes (‘shadow prices’) optimal solutions in constraint bounds. This is especially useful when constraints represent resource limitations.

Represented Coxeter matroids of types Cn and Dn, that is, symplectic and orthogonal matroids arising from totally isotropic subspaces of symplectic or (even-dimensional) orthogonal spaces, may also be represented in buildings of type Cn and Dn, respectively (see [4, Chapter 7]). Indeed, the particular buildings involved are those arising from the flags or oriflammes, respectively, of totally is...

The analytic center cutting plane method (ACCPM) is one of successful methods to solve nondifferentiable optimization problems. In this paper ACCPM is used for the first time in the vehicle routing problem with time windows (VRPTW) to accelerate lagrangian relaxation procedure for the problem. At first the basic cutting plane algorithm and its relationship with column generation method is clari...

The Lagrangian star is a germ of the system ({L1, . . . , Lk}, p̃) of Lagrangian submanifolds in the symplectic manifold (M,ω). We investigate the symplectic group action on Lagrangian stars and construct the basic invariants of such action. The Kashiwara signature for 3-Lagrangian linear stars is generalized to the nonlinear case and the generalized contact classes for Lagrangian stars are cons...

We develop the foundation of the complex symplectic geometry of Lagrangian subvarieties in a hyperkähler manifold. We establish a characterization, a Chern number inequality, topological and geometrical properties of Lagrangian submanifolds. We discuss a category of Lagrangian subvarieties and its relationship with the theory of Lagrangian intersection. We also introduce and study extensively a...

The purpose of this paper is to investigate the EGM method and the behavior of a solid particle suspended in a twodimensional rectangular cavity due to conjugate natural convection. A thermal lattice Boltzmann BGK model is implemented to simulate the two dimensional natural convection and the particle phase was modeled using the Lagrangian–Lagrangian approach where the solid particles are treat...

We also use soft methods from symplectic geometry (the relative version of the h–principle for Lagrangian immersions) and tools from algebraic topology to prove (both positive and negative) results about Lagrangian desingularizations of Lagrangian submanifolds with isolated singularities; we view the (Maslov-zero) Lagrangian desingularization problem as the natural soft analogue of the special ...

We consider deformations of singular Lagrangian varieties in symplectic spaces. We prove that a Lagrangian deformation of a Lagrangian complete intersection is analytically rigid provided that this is the case infinitesimally. This result solves a problem posed by Colin de Verdière concerning Lagrangian curves. Finally, we prove the coherence of the direct image sheaves of relative infinitesima...