George P Papavassilopoulos | National Technical University of Athens (original) (raw)

Papers by George P Papavassilopoulos

Journal of Parallel and Distributed Computing, Sep 1, 1997

A parallel method for globally minimizing a linear program with an additional reverse convex cons... more A parallel method for globally minimizing a linear program with an additional reverse convex constraint is proposed which combines the outer approximation technique and the cutting plane method. Basically p (≤n) processors are used for a problem with n variables and a globally optimal solution is found effectively in a finite number of steps. Computational results are presented for test problems with a number of variables up to 80 and 63 linear constraints (plus nonnegativity constraints). These results were obtained on a distributed-memory MIMD parallel computer, DELTA, by running both serial and parallel algorithms with double precision. Also, based on 40 randomly generated problems of the same size, with 16 variables and 32 linear constraints (plus x ≥ 0), the numerical results from different number processors are reported, including the serial algorithm's.

arXiv (Cornell University), Aug 31, 2020

In this paper, we present a game-theoretic model describing the voluntary social distancing durin... more In this paper, we present a game-theoretic model describing the voluntary social distancing during the spread of an epidemic. The payoffs of the agents depend on the social distancing they practice and on the probability of getting infected. We consider two types of agents, the non-vulnerable agents who have a small cost if they get infected, and the vulnerable agents who have a higher cost. For the modeling of the epidemic outbreak, we consider a variant of the SIR (Susceptible-Infected-Removed) model involving populations of susceptible, infected and removed persons of vulnerable and non-vulnerable types. The Nash equilibria of this social distancing game are studied. The main contribution of this work is the analysis of the case where the players, desiring to achieve a low social inequality, pose a bound on the variance of the payoffs. In this case, we introduce and characterize a notion of Generalized Nash Equilibrium (GNE) for games with a continuum of players. Through numerical studies, we show that inequality constraints result in a slower spread of the epidemic and an improved cost for the vulnerable players. Furthermore, it is possible that inequality constraints are beneficial for non-vulnerable players as well.

arXiv (Cornell University), May 26, 2021

Individual behaviors play an essential role in the dynamics of transmission of infectious disease... more Individual behaviors play an essential role in the dynamics of transmission of infectious diseases, including COVID-19. This paper studies a dynamic game model that describes the social distancing behaviors during an epidemic, assuming a continuum of players and individual infection dynamics. The evolution of the players' infection states follows a variant of the well-known SIR dynamics. We assume that the players are not sure about their infection state, and thus they choose their actions based on their individually perceived probabilities of being susceptible, infected or removed. The cost of each player depends both on her infection state and on the contact with others. We prove the existence of a Nash equilibrium and characterize Nash equilibria using nonlinear complementarity problems. We then exploit some monotonicity properties of the optimal policies to obtain a reduced-order characterization for Nash equilibrium and reduce its computation to the solution of a low-dimensional optimization problem. It turns out that, even in the symmetric case, where all the players have the same parameters, players may have very different behaviors. We finally present some numerical studies that illustrate this interesting phenomenon and investigate the effects of several parameters, including the players' vulnerability, the time horizon, and the maximum allowed actions, on the optimal policies and the players' costs.

arXiv (Cornell University), Mar 16, 2019

Iet Control Theory and Applications, Jul 7, 2011

This study deals with recursive state estimation for non-linear systems. A new set of s-points fo... more This study deals with recursive state estimation for non-linear systems. A new set of s-points for the unscented Kalman filter is proposed as well as a way to substitute a non-linear output with a linear one. The importance of the function of the state which must be estimated is also illustrated and also the need for taking it into account when designing the state estimator. Modebased estimators are proposed. All the suggested methods are compared with standard extended Kalman filter, unscented Kalman filter and particle filter with sampling importance resampling using simulations. The results show that the modifications proposed in some cases lead to considerable reduction in the estimation error.

arXiv (Cornell University), Jul 10, 2020

The spontaneous behavioral changes of the agents during an epidemic can have significant effects ... more The spontaneous behavioral changes of the agents during an epidemic can have significant effects on the delay and the prevalence of its spread. In this work, we study a social distancing game among the agents of a population, who determine their social interactions during the spread of an epidemic. The interconnections between the agents are modeled by a network

IFAC-PapersOnLine, Jul 1, 2017

This paper considers the problem of designing a Network such that a set of dynamic rules converge... more This paper considers the problem of designing a Network such that a set of dynamic rules converges as fast as possible to the Nash equilibrium in a class of repeated games, despite the attempt of a jammer to slow down the convergence by cutting a certain number of edges. Particularly we consider a class of quadratic games, motivated by the demand response problem in electricity markets. For a given network structure, a set of dynamic rules, based on approximate gradient decent is described. The convergence speed depends on the graph through a matrix which in turn depends on the graph Laplacian. The network design problem is formulated as a zero sum game between a network designer aiming to improve the convergence speed and a jammer who tries to deteriorate it. Simple heuristics for the designer and the jammer problems are proposed and a numerical example is presented.

IEEE Transactions on Automatic Control, Jul 1, 2017

In this work, we study Static and Dynamic Games on Large Networks of interacting agents, assuming... more In this work, we study Static and Dynamic Games on Large Networks of interacting agents, assuming that the players have some statistical description of the interaction graph, as well as some local information. Inspired by Statistical Physics, we consider statistical ensembles of games and define a Probabilistic Approximate equilibrium notion for such ensembles. A Necessary Information Complexity notion is introduced to quantify the minimum amount of information needed for the existence of a Probabilistic Approximate equilibrium. We then focus on some special classes of games for which it is possible to derive upper and/or lower bounds for the complexity. At first, static and dynamic games on random graphs are studied and their complexity is determined as a function of the graph connectivity. In the low complexity case, we compute Probabilistic Approximate equilibrium strategies. We then consider static games on lattices and derive upper and lower bounds for the complexity, using contraction mapping ideas. A LQ game on a large ring is also studied numerically. Using a reduction technique, approximate equilibrium strategies are computed and it turns out that the complexity is relatively low.

IFAC Proceedings Volumes, Jun 1, 1996

This paper presents numerical compub,Lions for solving the BMI problem. Four globa.l algorithms i... more This paper presents numerical compub,Lions for solving the BMI problem. Four globa.l algorithms includlng two pa.rallel algorithms are employed to solve l}, e BMI probl'!m by a sequence of concave minimization problems or d.c. programs vi.:l concave programming. The parallel algorithms with or based on a :5uitable pa.rtit.ion of an initial enc1 o~; ing ployhC(hon are more efl'ldent. tha.n the seri"l oncs. Computational experiences are r(:porled for randomly generat.ed BMI problems of small size.

arXiv (Cornell University), Nov 8, 2017

We study Max-Product and Max-Plus Systems with Markovian Jumps and focus on stochastic stability ... more We study Max-Product and Max-Plus Systems with Markovian Jumps and focus on stochastic stability problems. At first, a Lyapunov function is derived for the asymptotically stable deterministic Max-Product Systems. This Lyapunov function is then adjusted to derive sufficient conditions for the stochastic stability of Max-Product systems with Markovian Jumps. Many step Lyapunov functions are then used to derive necessary and sufficient conditions for stochastic stability. The results for the Max-Product systems are then applied to Max-Plus systems with Markovian Jumps, using an isomorphism and almost sure bounds for the asymptotic behavior of the state are obtained. A numerical example illustrating the application of the stability results on a production system is also given.

Energies, Apr 19, 2018

A decision support tool has been developed to evaluate energy-saving intervention investments for... more A decision support tool has been developed to evaluate energy-saving intervention investments for domestic buildings. Various potential interventions are considered, each affecting energy consumption and savings, as well as the total financial cost of the investment. The decision problem is formulated as a mixed-integer programming problem. The implemented methodologies increase the efficiency and efficacy of the solution algorithms and can be applied to most realistic cases. The tool allows users to customize the problem based on their own preferences and find the optimal combination of investments. Uncertainty complicating the decision process is addressed by using interval analysis; therefore, the robustness of the optimal decision can be evaluated to facilitate the decision-making process. A domestic building in the Mediterranean area is used as a case study to demonstrate the functionality of this tool and to evaluate the impact of the decision-maker's uncertainty on the optimal decision.

IEEE Transactions on Automatic Control, Oct 1, 1982

This paper studies a two-player Nash dynamic, discrete-time, linear-quadratic game under the so-c... more This paper studies a two-player Nash dynamic, discrete-time, linear-quadratic game under the so-called "one-step delay observation sharing pattern." It is shown that under very weak assumptions the solution exists and is unique and linear in the information.

IEEE Transactions on Automatic Control, 1997

We consider the problem of minimizing the rank of a positive semidefinite matrix, subject to the ... more We consider the problem of minimizing the rank of a positive semidefinite matrix, subject to the constraint that an affine transformation of it is also positive semidefinite. Our method for solving this problem employs ideas from the ordered linear complementarity theory and the notion of the least element in a vector lattice. This problem is of importance in many contexts, for example in feedback synthesis problems; such an example is also provided.

An examination is made of a stochastic dynamic discrete-time game, and the possibility of obtaini... more An examination is made of a stochastic dynamic discrete-time game, and the possibility of obtaining approximate Nash equilibria which result in Pareto outcomes is studied. The time horizon is infinite. In the context of a simple linear quadratic model strategies that may achieve the aforementioned aim are suggested, and several insights and results are discussed.<<ETX>>

Open journal of optimization, 2014

This paper presents a dynamic mathematical model of optimal leasing allocation of satellite bandw... more This paper presents a dynamic mathematical model of optimal leasing allocation of satellite bandwidth and services in terms of expected revenues and associated risk. This tool meets the need of a Satellite Operator to determine the optimal leasing policy of the available bandwidth. A methodology and a tool for techno-economic evaluation of satellite services are developed. The output of the tool enables the policy decisions to be customized by the attitude toward risk that the company wants to apply at each time period. The study is based on inputs concerning data and services from an existing Satellite Operator and addresses a real situation. Demand and pricing data have been gathered from the international market. The decision making tool is given in the setup of a decision tree presenting quantified alternative leasing policies and risks. Sensitivity analysis is also performed to measure the efficiency of the model.

A distributed asynchronous algorithm for minimizing a function with a nonstationary minimum over ... more A distributed asynchronous algorithm for minimizing a function with a nonstationary minimum over a constraint set is considered. The communication delays among the processors are assumed to be stochastic with Markovian character. Conditions which guarantee the mean square and almost sure convergence to the sought solution are presented. We also present an optimal routing application for a network that connects various U.S. cities. Results of the extensive simulation that we implemented assert the practical applicability of distributed asynchronous algorithms with stochastic delays. Comparison results for varying the probability distribution of these delays are provided. The impact of varying the communication delay bound and the stepsize is also assessed.

Several methods have been proposed for solving a d.c. programming problem, but very few have been... more Several methods have been proposed for solving a d.c. programming problem, but very few have been done on parallel approach. In this paper, three algorithms suitable for parallel implementation are presented to solve a d.c. problem via solving an equivalent concave minimization problem. To distribute the computation load as evenly as possible, a simplex subdivision process such as bisection, triangulation or other partition procedures of simplices (cf. [7]) will be employed. Some numerical test results are reported and comparison of these algorithms are given.

arXiv (Cornell University), Mar 13, 2014

A Linear Quadratic Deterministic Continuous Time Game with many symmetric players is considered a... more A Linear Quadratic Deterministic Continuous Time Game with many symmetric players is considered and the Linear Feedback Nash strategies are studied as the number of players goes to infinity. We show that under some conditions the limit of the solutions exists and can be used to approximate the case with a finite but large number of players. It is shown that in the limit each player acts as if he were faced with one player only, who represents the average behavior of the others.

This paper considers a decentralized adaptive control problem for a class of discrete-time multi-... more This paper considers a decentralized adaptive control problem for a class of discrete-time multi-input multi-output deterministic linear systems. It is shown that, under a weak coupling condition, the Projection Algorithm will ensure that the system inputs and outputs remain bounded for all time and that each controller can successfully make the corresponding output tracking error converge to zero.

Parallel Computing, Mar 1, 1993

Abstract We present a general linear model of asynchronous iterations, the communication delays o... more Abstract We present a general linear model of asynchronous iterations, the communication delays of which are stochastic with Markovian character. This model allows static or dynamic allocation of the iterate vector components to processors. It also allows simultaneous updating of the same vector component by multiple processors. Sufficient conditions under which the model of asynchronous iterations converges in the second moment (and in the mean) to the sought solution are provided. For the specialization of the Markov case when the communication delays are independent, identically distributed (i.i.d.), we provide sufficient conditions for convergence in the second moment and necessary and sufficient conditions for convergence in the mean.