In this paper, an impulsive boundary value problem on the half-line is considered and existence of solutions is proved using Minimization Principal and Mountain Pass Theorem.

In this note, we generalize the affine rank minimization problem and the vector cardinality minimization problem and show that the resulting generalized problem can be solved by solving a sequence of continuous concave minimization problems. In the case of the vector cardinality minimization problem, we show that it can be solved by solving the continuous concave minimization problem.

Evaluation of the reliability parameters in micro-grids based on renewable energy sources is one of the main problems that are investigated in this paper. Renewable energy sources such as solar and wind energy, battery as an energy storage system and fuel cell as a backup system are used to provide power to the electrical loads of the micro-grid. Loads in the micro-grid consist of interruptible...

Given n intervals on a line `, we consider the problem of moving these intervals on ` such that no two intervals overlap and the maximum moving distance of the intervals is minimized. The difficulty for solving the problem lies in determining the order of the intervals in an optimal solution. By interesting observations, we show that it is sufficient to consider at most n “candidate” lists of o...

A method of determining a lower bound for the graph bisection minimization problem is described. The bound is valid for weigthed graphs with edge and node weights. The approach is based on Lagrangian relaxation and was previously used for determining an upper bound on the independence number of a graph. The determination of the lower bound is done by solving a quadratic programming problem. A c...

Environmental, social and political pressures to limit the impacts associated with green house gas (GHG) emissions are mounting rapidly. To date there has been no or limited research which seeks to reduce emissions as the primary objective of a routing problem despite the fast growth and high impact of commercial vehicles. In the capacitated vehicle routing problem with time windows (VRPTW), it...