Table of Content

30 December 2016, Volume 4 Issue 4

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Continuous Optimization

Inexact Proximal Point Methods for Quasiconvex Minimization on Hadamard Manifolds

Nancy Baygorrea· Erik Alex Papa Quiroz ·Nelson Maculan

2016, 4(4):  397.  doi:10.1007/s40305-016-0133-3

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In this paper we present two inexact proximal point algorithms to solve
minimization problems for quasiconvex objective functions on Hadamard manifolds.
We prove that under natural assumptions the sequence generated by the algorithms
are well defined and converge to critical points of the problem. We also present an
application of the method to demand theory in economy.

Alternating Direction Method of Multipliers for Linear Programming

Bing-Sheng He· Xiao-Ming Yuan

2016, 4(4):  425.  doi:10.1007/s40305-016-0136-0

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Linear programming is the core problem of various operational research
problems. The dominant approaches for linear programming are simplex and interior
point methods. In this paper, we showthat the alternating direction method of multipliers
(ADMM), which was proposed long time ago while recently found more and more
applications in a broad spectrum of areas, can also be easily used to solve the canonical
linear programming model. The resulting per-iteration complexity is O(mn) where m
is the constraint number and n the variable dimension. At each iteration, there are m
subproblems that are eligible for parallel computation; each requiring only O(n) flops.
There is no inner iteration as well.We thus introduce the newADMMapproach to linear
programming, which may inspire deeper research for more complicated scenarios
with more sophisticated results.

Stochastic Optimization

N-policy for Mx/G/1 Unreliable Retrial G-Queue with Preemptive Resume and Multi-services

2016, 4(4):  437.  doi:10.1007/s40305-016-0128-0

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Bulk arrival retrial G-queue with impatient customers and multi-services
subject to server breakdowns has been analyzed. The system allows the arrival of
two types of customers: positive customers and negative customers in the system.
The negative customers make the server fail if they find the server in busy state,
whereas positive customers are served if the server is idle otherwise they join the
virtual pool of customers called orbit. The customers from the retrial orbit try their
chance again for the service. The customers have the option of obtaining more than one
service. Moreover, the customers are impatient and may renege from the system with
probability (1−r ). The server is sent for repair as soon as it breakdowns; after repair,
the service process starts again. Also, the server has the provision to initiate the service
when there areN customers accumulated in the system. Using supplementary variables
technique and generating functions, various performance measures like reliability
indices and long run probabilities have been obtained.

Continuous Optimization

An Exact l1 Penalty Approach for Interval-ValuedProgramming Problem

Anurag Jayswal · Jonaki Banerjee

2016, 4(4):  461.  doi:10.1007/s40305-016-0120-8

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The objective of this paper is to propose an exact l1 penalty method for
constrained interval-valued programming problems which transform the constrained
problem into an unconstrained interval-valued penalized optimization problem. Under
some suitable conditions, we establish the equivalence between an optimal solution of
interval-valued primal and penalized optimization problem. Moreover, saddle-point
type optimality conditions are also established in order to find the relation between an
optimal solution of penalized optimization problem and saddle-point of Lagrangian
function. Numerical examples are given to illustrate the derived results.

A Cutting Hyperplane Projection Method for Solving Generalized Quasi-Variational Inequalities

Ming-Lu Ye

2016, 4(4):  483.  doi:10.1007/s40305-016-0123-5

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Management Science

Structural Properties in a Hub-to-Hub Network Revenue Management Problem

Hong-Zhi He

2016, 4(4):  503.  doi:10.1007/s40305-016-0126-2

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In this paper, the structural properties of revenue management in a hubto-
hub airline network is studied. Using a reformulated network flow version of the
problem, it is shown that the optimal value has supermodularity, submodularity, and
L concavity in the network’s capacities dimensions. It is thus deduced that the certainty
equivalent control thresholds used in the revenue management problem have
monotone properties. These structural properties add important managerial insights
into the network revenue management system.

Discrete Optimization

The Shortest First Coordination Mechanism for a Scheduling Game with Parallel-Batching Machines

2016, 4(4):  517.  doi:10.1007/s40305-016-0134-2

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This paper deals with a scheduling problem with parallel-batching machines
from a game theoretic perspective. There are m parallel-batching machines, each of
which can handle up to b jobs simultaneously as a batch. The processing time of a
batch is the time required for processing the longest job in the batch, and all the jobs
in a batch start and complete at the same time. There are n jobs. Each job is owned by
a rational and selfish agent. The agent of a job chooses a machine for processing its
own job. The aim of each agent is to minimize the completion time of its job while the
system tries tominimize the maximal completion time over all jobs, the makespan.We
design a coordination mechanism for the scheduling game problem. We discuss the
existence of Nash equilibria of the mechanism and showthat it has a price of anarchy 2.