Luke Finlay

Defence Science and Technology Group

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Vladimir Gaitsgory

Macquarie University

Konstantin Avrachenkov

Institut national de recherche en informatique et en automatique

Ivan Lebedev

Eitan Altman

Laboratoire Informatique d'Avignon

Philippe Nain

Institut national de recherche en informatique et en automatique

Danil Nemirovsky

Institut national de recherche en informatique et en automatique

Evsey Morozov

Russian Academy of Sciences

A. Chockalingam

Indian Institute of Science Bangalore

Andrey Garnaev

Rutgers, The State University of New Jersey

Leon A. Petrosyan

St Petersburg University

Cooperative Institutions

Institut national de recherche en informatique et en automatique

Université Côte d'Azur

Research Centre Inria Sophia Antipolis - Méditerranée

Fondation Sophia Antipolis

St Petersburg University

Centre National de la Recherche Scientifique

Defence Science and Technology Group

Institut de Biologie Valrose

University of South Australia

Université d'Avignon et des Pays de Vaucluse

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Analysis of TCP-AQM Interaction Via Periodic Optimization and Linear Programming: The Case of Sigmoidal Utility Function

Lecture notes in computer science (2006)

Konstantin Avrachenkov Luke Finlay Vladimir Gaitsgory

Sigmoid function

Random early detection

10.1007/11759355_47

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Citations (3)

Linear programming solutions of periodic optimization problems: approximation of the optimal control

Journal of Industrial and Management Optimization (2007)

Luke Finlay Vladimir Gaitsgory Ivan Lebedev

Deterministic long run average problems of optimal control are ''asymptotically equivalent" to infinite-dimensional linear programming problems ( LPP ) and the latter are approximated by finite dimensional LPP. The solutions of this finite dimensional LPP can be used for numerical analysis of periodic optimization problems. In the present paper we establish the convergence of controls constructed on the basis of the solution of the finite dimensional LPP to the optimal control of a periodic optimization problem. Results are illustrated with a numerical example.

10.3934/jimo.2007.3.399

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Citations (12)

Duality in Linear Programming Problems Related to Deterministic Long Run Average Problems of Optimal Control

SIAM Journal on Control and Optimization (2008)

Luke Finlay Vladimir Gaitsgory Ivan Lebedev

It has been established recently that, under mild conditions, deterministic long run average problems of optimal control are “asymptotically equivalent” to infinite-dimensional linear programming problems (LPPs) and that these LPPs can be approximated by finite-dimensional LPPs. In this paper we introduce the corresponding infinite- and finite-dimensional dual problems and study duality relationships. We also investigate the possibility of using solutions of finite-dimensional LPPs and their duals for numerical construction of the optimal controls in periodic optimization problems. The construction is illustrated with a numerical example.

Duality (order theory)

Dual polyhedron

10.1137/060676398

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Citations (27)

Online LIB problems: Heuristics for Bin Covering and lower bounds for Bin Packing

RAIRO - Operations Research (2005)

Luke Finlay Prabhu Manyem

We consider the NP Hard problems of online Bin Covering and Packing while requiring that larger (or longer, in the one dimensional case) items be placed at the bottom of the bins, below smaller (or shorter) items — we call such a version, the LIB version of problems. Bin sizes can be uniform or variable. We look at computational studies for both the Best Fit and Harmonic Fit algorithms for uniform sized bin covering. The Best Fit heuristic for this version of the problem is introduced here. The approximation ratios obtained were well within the theoretical upper bounds. For variable sized bin covering, a more thorough analysis revealed definite trends in the maximum and average approximation ratios. Finally, we prove that for online LIB bin packing with uniform size bins, no heuristic can guarantee an approximation ratio better than 1.76 under the online model considered.

Bin packing problem

Heuristics

Best bin first

Online algorithm

10.1051/ro:2006001

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Citations (11)

Models for Performance Analysis and Control of Networks

Philippe Nain Eitan Altman Ephie Deriche Sara Alouf Konstantin Avrachenkov

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Panel Discussion: Foreign Governmental Control of Multinational Corporations Marketing in the United States

Syracuse journal of international law and commerce (1974)

John D. Beach Joseph P. Griffin Michael W. Gordon Luke Finlay

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TCP-AQM Interaction: Periodic Optimization via Linear Programming

Springer eBooks (2006)

Konstantin Avrachenkov Luke Finlay Vladimir Gaitsgory

Explicit Congestion Notification

Random early detection

10.1007/0-387-33815-2_1

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Citations (2)

Duality in linear programming problems related to deterministic long run average problems of optimal control with applications to periodic optimization

Luke Finlay Vladimir Gaitsgory Ivan Lebedev

Deterministic long run average optimal control problems and, in particular, periodic optimization problems are related to certain infinite-dimensional linear programming (LP) problems, which can be approximated by finite-dimensional LP problems. In this paper we study problems dual to these infinite- and finite- dimensional LP problems, and we investigate a possibility of using solutions of the latter for numerical construction of the optimal controls in periodic optimization problems. The construction is illustrated with a numerical example.

Duality (order theory)

10.1109/cdc.2009.5400261

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Citations (1)

Analysis of TCP-AQM interaction via periodic optimization and linear programming : The case of sigmoidal utility function

Lecture notes in computer science (2006)

Konstantin Avrachenkov Luke Finlay Vladimir Gaitsgory

Sigmoid function

Random early detection

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