Optimization of Stochastic Discrete Systems and Control on Complex Networks

1. Front Matter

   Pages i-xix

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2. Discrete Stochastic Processes, Numerical Methods for Markov Chains and Polynomial Time Algorithms

   • Dmitrii Lozovanu, Stefan Pickl

   Pages 1-102

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3. Stochastic Optimal Control Problems and Markov Decision Processes with Infinite Time Horizon

   • Dmitrii Lozovanu, Stefan Pickl

   Pages 103-211

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4. A Game-Theoretical Approach to Markov Decision Processes, Stochastic Positional Games and Multicriteria Control Models

   • Dmitrii Lozovanu, Stefan Pickl

   Pages 213-339

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5. Dynamic Programming Algorithms for Finite Horizon Control Problems and Markov Decision Processes

   • Dmitrii Lozovanu, Stefan Pickl

   Pages 341-388

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6. Errata to: Optimization of Stochastic Discrete Systems and Control on Complex Networks

   • Dmitrii Lozovanu, Stefan Pickl

   Pages E1-E4

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7. Back Matter

   Pages 389-400

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This book presents the latest findings on stochastic dynamic programming models and on solving optimal control problems in networks. It includes the authors’ new findings on determining the optimal solution of discrete optimal control problems in networks and on solving game variants of Markov decision problems in the context of computational networks. First, the book studies the finite state space of Markov processes and reviews the existing methods and algorithms for determining the main characteristics in Markov chains, before proposing new approaches based on dynamic programming and combinatorial methods. Chapter two is dedicated to infinite horizon stochastic discrete optimal control models and Markov decision problems with average and expected total discounted optimization criteria, while Chapter three develops a special game-theoretical approach to Markov decision processes and stochastic discrete optimal control problems. In closing, the book’s final chapter is devoted to finite horizon stochastic control problems and Markov decision processes. The algorithms developed represent a valuable contribution to the important field of computational network theory.

• Complex networks
• Discrete optimal control
• Game theory
• Linear programming
• Markov decision process
• Stochastic dynamic programming
• algorithm analysis and problem complexity

“This book contributes to the systematization of the most relevant existing methods for these problems by introducing new algorithms for solving different classes of stochastic dynamic programming problems. … The mathematical and computational level of the book will enable students and practitioners to deepen their understanding of the topic. Numerous examples are included to illustrate the proposed algorithms and methods.” (Rosario Romera, Mathematical Reviews, July, 2015)

• Academy of Sciences of Moldova Institute of Mathematics & Informatics, Chisinau, Moldova

  Dmitrii Lozovanu

• Universität der Bundeswehr München, Institut für Theoretische Informatik, Mathematik und Operations Research,, Munchen, Germany

  Stefan Pickl

Prof. Dr. Stefan Pickl is professor for Operations Research at Universität der Bundeswehr in Munich. He studied mathematics, electrical engineering, and philosophy at TU Darmstadt and EPFL Lausanne 1987-93. Dipl.-Ing. '93, Doctorate 1998 with award. Assistant Professor at Cologne University (Dr. habil. 2005; venia legendi ``Mathematics"). Visiting Professor at University of New Mexico (U.S.A.), University Graz (Austria), University of California at Berkeley. Visiting scientist at SANDIA, Los Alamos National Lab, Santa Fe Institute for Complex Systems and MIT. Associated with Centre for the Advanced Study of Algorithms (CASA, USA) and Center for Network Innovation and Experimentation (CENETIX, USA) , vice-chair of EURO group ``Experimental OR”, program for highly gifted pupils, research program``Intelligent Networks and Security Structures” (INESS), ``Critical Infrastructures and System Analyses" (CRISYS). International best paper awards ’03, ’05, '07. Foundation of COMTESSA (Competence Center for Operations Research, Strategic Planning Management, Safety & Security ALLIANCE).

Prof. Dr. Dmitrii Lozovanu received his PhD in mathematics  in 1980 from the Institute of Cybernetics of Academy of Sciences of Ukraine, Kiev. After the habilitation theses defense in 1991 he became professor in Computer Science. He is the head of department of Applied Mathematics at the Faculty of Mathematics and Computer Science of Moldova State University, Chisinau. His research interest

s are related to discrete optimization, game theory, optimal control and stochastic decision processes.

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