Algorithms for the constrained bottleneck matroid base problem and the constrained bottleneck independent set problem are presented. The algorithms have improved complexities upon the best known general algorithm. Sufficient conditions are obtained when the proposed algorithms have linear complexity and are therefore the best possible ones. Several specific classes of matroidal problems are con...

The Object Allocation Problem (OAP) is a well studied problem which is about to allocate a set X of n objects to a set N of n agents. This paper deals with a generalization called Constrained Object Allocation Problem (COAP) where the set of objects allocated to the agents must satisfy a given feasibility constraint. The input is a set X of at least n elements and a collection S of subsets of X...

In this paper, a new numerical method is presented for solving the optimal control problems of Bang-Bang type with free or fixed terminal time. The method is based on Bezier polynomials which are presented in any interval as $[t_0,t_f]$. The problems are reduced to a constrained problems which can be solved by using Lagrangian method. The constraints of these problems are terminal state and con...

The aim of this paper is to study the convergence properties of the gradient projection method and to apply these results to algorithms for linearly constrained problems. The main convergence result is obtained by defining a projected gradient, and proving that the gradient projection method forces the sequence of projected gradients to zero. A consequence of this result is that if the gradient...

In the paper a view, based on the optimization approach, is given on different types of constrained clustering problems and methods for their solution.

In many applications it is necessary to find a minimum weight assignment that satisfies one or several additional resource constraints. For example, consider the problem of assigning persons to jobs where each assignment utilizes at least two scarce resources and the resource utilization is dependent on the person and the type of task. A practical situation where the above might occur is a slau...

Splitting off two edges su, sv in a graph G means deleting su, sv and adding a new edge uv. Let G = (V + s,E) be k-edge-connected in V (k ≥ 2) and let d(s) be even. Lovász proved that the edges incident to s can be split off in pairs in a such a way that the resulting graph on vertex set V is k-edge-connected. In this paper we investigate the existence of such complete splitting sequences when ...

This paper starts by discussing an algorithmic view of labeled path problems. In particular, we apply Seidel’s all-pairs shortest-path algorithm for undirected and unweighted graphs to a basic problem in labeled paths. Seidel’s algorithm is applied to find unlabeled paths between any pairs of nodes in a labeled graph whose associated context-free grammar G can generate the empty string . Our re...

The integral representation for the relaxation of a class of energy functionals where the admissible fields are constrained to remain on a C m-dimensional manifold M ⊂ R is obtained. If f : Rd×N → [0,∞) is a continuous function satisfying 0 ≤ f(ξ) ≤ C(1 + |ξ|), for C > 0, p ≥ 1, and for all ξ ∈ Rd×N , then F(u,Ω) : = inf {un}  lim inf n→∞ Z Ω f(∇un) dx : un ⇀ u in W , un(x) ∈M a.e. x ∈ Ω, n ∈ ...