Search results for "Mathematical optimization"

Table of periodic properties of human immunodeficiency virus inhibitors

2010

Classification algorithms are proposed based on information entropy. The feasibility of mixing a given human immunodeficiency virus (HIV) inhibitor with dissimilar ones is studied. The 31 inhibitors are classified by their structural chemical properties. Many classification algorithms are based on information entropy. An excessive number of results appear compatible with the data and suffer combinatorial explosion. However, after the equipartition conjecture one has a selection criterion. According to this conjecture, the best configuration is that in which entropy production is most uniformly distributed. The structural elements of an inhibitor can be ranked according to their inhibitory a…

Multilevel preconditioning and adaptive sparse solution of inverse problems

2012

Continuous reformulations and heuristics for the Euclidean travelling salesperson problem

2008

We consider continuous reformulations of the Euclidean travelling salesperson problem (TSP), based on certain clustering problem formulations. These reformulations allow us to apply a generalisation with perturbations of the Weiszfeld algorithm in an attempt to find local approximate solutions to the Euclidean TSP.

Global convergence and rate of convergence of a method of centers

1994

We consider a method of centers for solving constrained optimization problems. We establish its global convergence and that it converges with a linear rate when the starting point of the algorithm is feasible as well as when the starting point is infeasible. We demonstrate the effect of the scaling on the rate of convergence. We extend afterwards, the stability result of [5] to the infeasible case anf finally, we give an application to semi-infinite optimization problems.

A Posteriori Error Bounds for Approximations of the Oseen Problem and Applications to the Uzawa Iteration Algorithm

2014

Abstract. We derive computable bounds of deviations from the exact solution of the stationary Oseen problem. They are applied to approximations generated by the Uzawa iteration method. Also, we derive an advanced form of the estimate, which takes into account approximation errors arising due to discretization of the boundary value problem, generated by the main step of the Uzawa method. Numerical tests confirm our theoretical results and show practical applicability of the estimates.

Online Pricing via Stackelberg and Incentive Games in a Micro-Grid

2019

This paper deals with the analysis and design of online pricing mechanisms in micro-grids. Two cases are studied in which the market layer is modeled as an open-loop and closed-loop dynamical system respectively. In the case of open-loop market dynamics, the price is generated as equilibrium price of a Stackelberg game with an incentive strategy. In such Stackelberg game, the leader is the energy supplier, the follower is the consumer, and the leader plays an incentive strategy. In the case of closed-loop market dynamics, the price is obtained as a function of the power supplied and the demand. A stability analysis is provided for both cases, which sheds light on the transient and steady-st…

On the Coincidence of the Feedback Nash and Stackelberg Equilibria in Economic Applications of Differential Games

2002

In this paper the scope of the applicability of the Stackelberg equilibrium concept in differential games is investigated. Firstly, conditions for obtaining the coincidence between the Stackelberg and Nash equilibria are defined in terms of the instantaneous pay-off function and the state equation of the game. Secondly, it is showed that for a class of differential games with state-interdependence both equilibria are identical independently of the player being the leader of the game. A survey of different economic models shows that this coincidence is going to occur for a good number of economic applications of differential games. This result appears because of the continuous-time setting i…

Constrained consensus for bargaining in dynamic coalitional TU games

2011

We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. We assume that the players in the game interact only with their neighbors, where the neighbors may vary over time. The main contributions of the paper are the definition of a robust (coalitional) TU game and the development of a distributed bargaining protocol. We prove the convergence with probability 1 of the bargaining protocol to a random allocation that lies in the core of the robust game under some mild conditions on the players' communication graphs.

Non-cooperative power allocation game with imperfect sensing information for cognitive radio

2012

In this paper, we consider a sensing-based spectrum sharing scenario and present an efficient decentralized algorithm to maximize the total throughput of the cognitive radio users by optimizing jointly both the detection operation and the power allocation, taking into account the influence of the sensing accuracy. This optimization problem can be formulated as a distributed non-cooperative power allocation game, which can be solved by using an alternating direction optimization method. The transmit power budget of the cognitive radio users and the constraint related to the rate-loss of the primary user due to the interference are considered in the scheme. Finally, we use variational inequal…

Efficient Parallel Nash Genetic Algorithm for Solving Inverse Problems in Structural Engineering

2015

A parallel implementation of a game-theory based Nash Genetic Algorithm (Nash-GAs) is presented in this paper for solving reconstruction inverse problems in structural engineering. We compare it with the standard panmictic genetic algorithm in a HPC environment with up to eight processors. The procedure performance is evaluated on a fifty-five bar sized test case of discrete real cross-section types structural frame. Numerical results obtained on this application show a significant achieved increase of performance using the parallel Nash-GAs approach compared to the standard GAs or Parallel GAs.