Proximal Point Methods (PPM) can be traced to the pioneer works of Moreau [16], Martinet [14,15] and Rockafellar [19, 20] who used as regularization function the square of the Euclideannorm. In this work, we study PPM in the context of optimization and we derive a class of suchmethods which contains Rockafellar's result. We also present a less stringent criterion to theacceptance of an approximate solution to the subproblems that arise in the inner loops of PPM.Moreover, we introduce a new family of augmented Lagrangian methods for convex constrainedoptimization, that generalizes the PE+ class presented in [2].

The present study proposes an extended opportunity-basedage replacement policy where opportunities occur according to a Poissonprocess. When the age, x of the system satisfies x < S for aprespecified value S, a corrective replacement is conducted if theobjective system fails. In case x satisfies S ≤ x < T foranother prespecified value T, we take an opportunity to preventivelyreplace the system by a new one with probability p, and do not takethe opportunity with probability 1 - p. At the moment x reaches T,a preventive replacement is executed independently of opportunities. Thelong-term average cost of the proposed policy is formulated. Theconditions under which optimal values for S and T exist for aprespecified value of T and S, respectively, are then clarified. Numerical examples are also presented to illustrate the theoreticalunderpinnings of the proposed replacement policy formulation.

The main purpose of this paper is to give a method forconstruction of the reduced reachability graph for Stochastic Petri Nets(SPN), the symbolic graph. This construction is achieved by exploitingthe structural symetries in the net using the theory of bisimulation ofplaces for detecting isomorphic parts in the net. The symbolic graph,being isomorphic to an agregated Markov chain, may be used to provequalitative properties as liveness, boundness, ... Moreover, thisreduced graph make more easy the computation of the performance measuresof interest as the mean number of tokens in a place, the mean number offiring transition ... We have so developped a tool, SSPN (StochasticSymetric Petri nets), for generating the symbolic graph and deducingqualitatives and quantitatives properties.

We focus on performance study of routers in high-speednetwork through a queuing network analytical model. Such a model givesaccurate results about classical performance criteria. For example,analytical study of packet loss probabilities in a router uses aproduct-form queuing network. The analytical results are compared tosimulation results, and they provide routers managers with invaluableinformation for internal memories tuning.

In this paper, we present a new linear time algorithm forscheduling UECT (Unit Execution and Communication Time) trees on twoidentical processors. The chosen criterion is the makespan. The used strategy is based on clustering of tasks. We show that this algorithm builds optimal schedules. Some extensions are discussed for non UECT tasks.

In this paper we give the expression of the multiplecorrelation coefficient in a linear model according to the coefficientsof correlation. This expression makes it possible to analyze from anumerical point of view the instability of estimates in the case ofcollinear explanatory variables in the linear model or in theautoregressive model. This numerical approach, that we show on twoexamples, thus supplements the usual approach of the quasi colinearity,founded on the statistical properties of the estimators.

Most location problems on networks consider discretenodal demand. However, for many problems, demands are betterrepresentedby continuous functions along the edges, in addition to nodaldemands. Several papers consider the optimal location problemof one or more facilities when demands are continuously distributedalong the network, and the objective function dealt with is themedian one. Nevertheless, in location of public services itis desirable to use an equity criterion. One of the latter is varianceofdistance distribution which has been studied only for discrete nodaldemands. In this paper the variance problem has been generalizedto the case where one allows the demand to arisediscretely on the nodes as well as continuously along the edges. Properties and behaviour of the objective function arestudied. Likewise we present an exact algorithm forsolving this problem in a network, which reduces the complexityof the exhaustive procedure.

The solution of a variety of classes of globaloptimisation problemsis required in theimplementation of a framework for sensitivity analysis in multicriteria decision analysis. These problems have linear constraints, some of which have a particularstructure, anda variety of objective functions, which may be smooth or non-smooth. Thecontext in which theyarise implies a need for a single, robust solution method.The literature contains few experimental results relevant to such aneed.We report on our experience with the implementation of threestochastic algorithms for global optimisation: the multi-level singlelinkage algorithm,the topographical algorithm and the simulated annealing algorithm.Issues relating to their implementation and use to solve practicalproblems are discussed. Computational results suggest that, for the class of problems considered, simulated annealing performs well.