We propose new techniques for the solution of the LP relaxation and the Lagrangean dual in combinatorial optimization problems. Our techniques find the optimal solution value and the optimal dual multipliers of the LP relaxation and the Lagrangean dual in polynomial time using as a subroutine either the Ellipsoid algorithm or the recent algorithm of Vaidya. Moreover, in problems of a certain st...

We provide sufficient conditions on the objective functional and the constraint functions under which the Lagrangean can be represented by a ` sequence of multipliers in infinite horizon discrete time optimal growth models.

We introduce a mathematical model and new Lagrangean numerical algorithm for modelling of a wind-driven forest fire front propagation. The model is based on evolution of plane curve (representing the fire front) in the outer normal direction by a speed given by the properties of a fuel bed which is scaled exponentially by a wind speed projected onto the normal to the front. The influence of the...

We follow the popular approach for unconstrained minimization, i.e. we develop a local quadratic model at a current approximate minimizer in conjunction with a trust region. We then minimize this local model in order to nd the next approximate minimizer. Asymptot-ically, nding the local minimizer of the quadratic model is equivalent to applying Newton's method to the stationarity condition. For...

A new passive wheel type leg-wheeled hybrid mobile robot based on surface motion principle was introduced. To produce the propulsion force, a passive wheel was installed at the end of the parallel mechanism structured leg connecting with the frame-body to make the wheel vertical to the ground at any time. With the inertia framework, the robot framework and some assumptions, two forms of Maggie ...

In this paper, we attempt to solve the problem of min-cost multicast routing for multi-layered multimedia distribution. More specifically, for (i) a given network topology (ii) the destinations of a multicast group and (iii) the bandwidth requirement of each destination, we attempt to find a feasible routing solution to minimize the cost of a multicast tree for multi-layered multimedia distribu...

We study the Job-Shop Scheduling problem with Earliness and Tardiness penalties. We describe two Lagrangean relaxations of the problem. The ̄rst one is based on the relaxation of precedence constraints while the second one is based on the relaxation of machine constraints. We introduce dedicated algorithms to solve the corresponding dual problems. The second one is solved by a simple dynamic pr...