Real-variable methods are used to prove the Marcinkiewicz Interpolation Theorem, boundedness of the dyadic and Hardy-Littlewood maximal operators, and the Calderón-Zygmund Covering Lemma. The Hilbert transform is defined, and its boundedness is investigated. All results lead to a final theorem on the pointwise convergence of the truncated Hilbert transform

abstract one of the basic assumptions in hub covering problems is considering the covering radius as an exogenous parameter which cannot be controlled by the decision maker. practically and in many real world cases with a negligible increase in costs, to increase the covering radii, it is possible to save the costs of establishing additional hub nodes. change in problem parameters during the pl...

In this paper we develop a new primal-dual subgradient method for nonsmooth convex optimization problems. This scheme is based on a self-concordant barrier for the basic feasible set. It is suitable for finding approximate solutions with certain relative accuracy. We discuss some applications of this technique including fractional covering problem, maximal concurrent flow problem, semidefinite ...

This paper studies a covering problem on graph which is a variant of facility location problem. In this research, constraints are considered to improve the previous model. These constraints have not considered previously. The first constraint limits the capacity of the facilities and the other one considers different coverage distances. The objective is to determine the optimal subset of candid...

This paper presents a hybrid algorithm that combines a metaheuristic and an exact method to solve the Probabilistic Maximal Covering Location-Allocation Problem. A linear programming formulation for the problem presents variables that can be partitioned into location and allocation decisions. This model is solved to optimality for small and medium-size instances. To tackle larger instances, a f...

Public transit service is a promising travel mode because of its potential to address urban sustainability. However, current ridership of public transit is very low in most urban regionsö particularly those in the United States. Low transit ridership can be attributed to many factors, among which poor service quality is key. Transit service quality may potentially be improved by decreasing the ...

We compare heuristics based on Lagrangean and surrogate relaxations of the Maximal Covering Location Problem (MCLP). The Lagrangean relaxation of MCLP used in this paper has the integrality property and the surrogate relaxed problem we solve is the LP relaxation of the original 0ÿ1 knapsack problem. The heuristics were compared using 331 test problems available in the literature, corresponding ...

Capacitated covering models aim at covering the maximum amount of customers’ demand using a set of capacitated facilities. Based on the assumptions made in such models, there is a unique scenario to open a facility in which each facility has a pre-specified capacity and an operating budget. In this paper, we propose a generalization of the maximal covering location problem, in which facilities ...

The Maximal Covering Location Problem (MCLP) has the objective of maximizing the total demand volume covered by a facility within a maximum allowable travel distance, S. In this paper, three sets of data 30-node, 324-node and 818-node networks with no existing facilities are analyzed as the capacitated model of MCLP (CMCLP) and first solved by the commercial optimization software, CPLEX. As the...

Abstract: Hub location problem is one of the most important problems in the areas of logistics and telecommunication network design. In this paper, we address the single allocation maximal covering hub location problem in which the objective is to maximise the amount of covered flows associated with origin-destination pairs in a hub-and-spoke network using a fixed number of hub facilities. Two ...