The optimal control problem for a class of hybrid systems (switched Lagrangian systems) is studied. Some necessary conditions of the optimal solutions of such a system are derived based on the assumption that there is a group of symmetries acting uniformly on the domains of different discrete modes, such that the Lagrangian functions, the guards, and the reset maps are all invariant under the a...

Constraint propagation is inherently restricted to the local information that is available to each propagator. We propose to improve the communication between constraints by introducing Lagrangian penalty costs between pairs of constraints, based on the Lagrangian decomposition scheme. The role of these penalties is to force variable assignments in each of the constraints to correspond to one a...

We consider solving nonlinear programming problems using an augmented Lagrangian method that makes use of derivative-free generating set search to solve the subproblems. Our approach is based on the augmented Lagrangian framework of Andreani, Birgin, Mart́ınez, and Schuverdt which allows one to partition the set of constraints so that one subset can be left explicit, and thus treated directly wh...

In this paper, we consider the working VP and backup VP routing problems jointly and employ the integer programming based approach to maximize the system resource utilization and the network survivability. The VP planning problem is formulated as a nonlinear combinatorial optimization problem. The objective function minimizes the resource usage while maximizing the network survivability. By pro...

We are considering the application of the Augmented Lagrangian algorithms with quadratic penalty, to convex problems of quadratic programming. The problems of quadratic programming are composites of quadratic objective function and linear constraints. This important class of problems will be generated through the algorithm of sequential quadratic programming, where at each iteration the quadrat...

A mechanism amenable to laminate and fold flows is identified and quantified. This laminating mechanism follows from a physical and experimental approach relying on the interlaced structure of velocity and Lagrangian acceleration. The Lagrangian acceleration being the resultant of the forces applied on particle fluids, the component of acceleration perpendicular to the velocity vector allows th...

We propose a geometric approach to the BRST-symmetries of the Lagrangian of a topological quantum field theory on a four dimensional manifold based on the formalism of superconnections. Making use of a graded q-differential algebra, where q is a primitive N -th root of unity, we also propose a notion of ZN -connection which is a generalization of a superconnection. In our approach the Lagrangia...

We discuss a Lagrangian-relaxation-based heuristics for dealing with feature selection in a standard L1 norm Support Vector Machine (SVM) framework for binary classification. The feature selection model we adopt is a Mixed Binary Linear Programming problem and it is suitable for a Lagrangian relaxation approach. Based on a property of the optimal multiplier setting, we apply a consolidated nons...

Finite-time coherent sets inhibit mixing over finite times. The most expensive part of the transfer operator approach to detecting coherent sets is the construction of the operator itself. We present a numerical method based on radial basis function collocation and apply it to a recent transfer operator construction [G. Froyland, "Dynamic isoperimetry and the geometry of Lagrangian coherent str...

We develop an alternative approach to study the effect of the generic perturbation (in addition to explicitly considering the loss term) in the nonlinear Klein-Gordon equations. By a change of the variables that cancel the dissipation term we are able to write the Lagrangian density and then, calculate the Lagrangian as a function of collective variables. We use the Lagrangian formalism togethe...