rates of convergence for a class of global stochastic optimization algorithms inspired and motivated by the recent advances in simulated annealing algorithms this paper analyzes the convergence rates of a class of recursive algorithms for global optimization via monte carlo methods by using perturbed liapunov function methods stability results of the algorithms are established then the rates of convergence are ascertained by examining the asymptotic properties of suitably scaled estimation error sequences

on a multistage discrete stochastic optimization problem with stochastic constraints and nested sampling we consider a multistage stochastic discrete program in which constraints on any stage might involve expectations that cannot be computed easily and are approximated by simulation we study a sample average approximation saa approach that uses nested sampling in which at each stage a number of scenarios are examined and a number of simulation replications are performed for each scenario to estimate the next stage constraints this approach provides an approximate solution to the multistage problem to establish the consistency of the saa approach we first consider a two stage problem and show that in the second stage problem given a scenario the optimal values and solutions of the saa converge to those of the true problem with probability one when the sample sizes go to infinity these convergence results do not hold uniformly over all possible scenarios for the second stage problem we are nevertheless able to prove that the optimal values and solutions of the saa converge to the true ones with probability one when the sample sizes at both stages increase to infinity we also prove exponential convergence of the probability of a large deviation for the optimal value of the saa the true value of an optimal solution of the saa and the probability that any optimal solution to the saa is an optimal solution of the true problem all of these results can be extended to a multistage setting and we explain how to do it our framework and saa results cover a large variety of resource allocation problems for which at each stage after the first one new information becomes available and the allocation can be readjusted under constraints that involve expectations estimated by monte carlo as an illustration we apply this saa method to a staffing problem in a call center in which the goal is to optimize the numbers of agents of each type under some constraints on the quality of service qos the staffing allocation has to be decided under an uncertain arrival rate with a prior distribution in the first stage and can be adjusted at some additional cost when better information on the arrival rate becomes available in later stages

fuzzy initial convergence structure abstract we introduce the notion of fuzzy initial convergence structure induced by family of functions the notion of fuzzy initial convergence structure is shown to be a generalization of fuzzy product convergence structure

fuzzy t net theory abstract in this paper we define the convergence of fuzzy nets in a fuzzy topological space x by means of the family of its level topologies l t t 0 1 introduced in 4 by lowen fuzzy t nets and fuzzy t ultranets are also characterized and relations between t prefilters and fuzzy t nets are studied getting analogous results to those of general topology

t prefilter theory abstract in the first part of this paper the notion of t prefilter is introduced and studied as are the applications t and t their properties and relations between them we characterize the minimal prime t prefilters finer than a given t prefilter by using ultrafilters on x and we give equivalents conditions of the t maximality in the second part we define t convergence and we obtain a characterization of t compactness gantner steinlage by means of the maximal t prefilters finally some applications of these concepts related to the continuity separation axioms and fuzzy compactness are studied

approximating an optimal production policy in a continuous flow line recurrence and asymptotic properties this work is concerned with manufacturing systems with two failure prone tandem machines the production is regulated by a continuous version of buffer control our goal is to obtain an optimal buffer control policy to minimize a long run average cost function concentrating on threshold type of control policies our effort is devoted to parameter optimization problems for the continuous material produce to stock models we estimate the gradients of the cost function with respect to the parameter using perturbation analysis techniques and approximate the optimal value of the parameter via a constant step size stochastic approximation algorithm an analysis for error accumulation in perturbation propagation is undertaken and a sufficient condition for breaking the propagation chain is derived in addition we show that the event of breaking the perturbation propagation chain is recurrent if the system has sufficient capacity derive the consistency of the gradient estimators and establish the convergence of the iterative algorithm we also treat non markovian models with the machine repair time following an erlang distribution and provide numerical examples to illustrate the proposed algorithm

analyzing convergence and rates of convergence of particle swarm optimization algorithms using stochastic approximation methods recently much progress has been made on particle swarm optimization pso a number of works have been devoted to analyzing the convergence of the underlying algorithms nevertheless in most cases rather simplified hypotheses are used for example it often assumes that the swarm has only one particle in addition more often than not the variables and the points of attraction are assumed to remain constant throughout the optimization process in reality such assumptions are often violated moreover there are no rigorous rates of convergence results available to date for the particle swarm to the best of our knowledge in this paper we consider a general form of pso algorithms and analyze asymptotic properties of the algorithms using stochastic approximation methods we introduce four coefficients and rewrite the pso procedure as a stochastic approximation type iterative algorithm then we analyze its convergence using weak convergence method it is proved that a suitably scaled sequence of swarms converge to the solution of an ordinary differential equation we also establish certain stability results moreover convergence rates are ascertained by using weak convergence method a centered and scaled sequence of the estimation errors is shown to have a diffusion limit

a new approach to fuzzy bitopological spaces abstract given a fuzzy bitopological space x 1 2 we have used the operator c12 ix ix defined by c 12 1 cl 2 cl i x which is a supra fuzzy closure operator fuzzy sets and systems 74 1995 353 to generate a family s which is a supra fuzzy topology loc cit 1995 so the space x s is a supra fuzzy topological space associated to the fuzzy bitopological space x 1 2 we extend the notions of fti strong fti and ultra fti due to fuzzy sets and system 43 1991 95 to the space x s the properties of fuzzy bitopological spaces have been studied by using their associated supra fuzzy topological spaces we introduce the notions of fp ti s fp ti and u fp ti by using the level supratopology s of s we investigate the relationship between these notions the notions fp ti loc cit 1995 i 1 2 3 4 and the notions fpti resp s fpti u fpti fuzzy sets and systems 105 1999 459 we give a number of examples which illustrate that these concepts are not equivalent also we extend the notions of f continuous open strong f continuous open and ultra f continuous open due to fuzzy sets and systems 38 1990 115 to the class of supra fuzzy topological spaces associated to the class of fuzzy bitopological spaces we study some properties of fp ti resp s fp ti u fp ti under these mappings

a review of regenerative processes the authors present an expository review of the theory of regenerative processes starting with the more traditional notions and then moving on to some of the more recent and modern developments fi

a simulation based approach to two stage stochastic programming with recourse in this paper we consider stochastic programming problems where the objective function is given as an expected value function we discuss monte carlo simulation based approaches to a numerical solution of such problems in particular we discuss in detail and present numerical results for two stage stochastic programming with recourse where the random data have a continuous multivariate normal distribution we think that the novelty of the numerical approach developed in this paper is twofold first various variance reduction techniques are applied in order to enhance the rate of convergence successful application of those techniques is what makes the whole approach numerically feasible second a statistical inference is developed and applied to estimation of the error validation of optimality of a calculated solution and statistically based stopping criteria for an iterative alogrithm 1998 the mathematical programming society inc published by elsevier science b v

stochastic optimization by simulation convergence proofs for the gi g 1 queue in steady state approaches like finite differences with common random numbers infinitesimal perturbation analysis and the likelihood ratio method have drawn a great deal of attention recently as ways of estimating the gradient of a performance measure with respect to continuous parameters in a dynamic stochastic system in this paper we study the use of such estimators in stochastic approximation algorithms to perform so called single run optimizations of steady state systems under mild conditions for an objective function that involves the mean system time in a gi g 1 queue we prove that many variant of these algorithms converge to the minimizer in most cases however the simulation length must be increased from iteration to iteration otherwise the algorithm may converge to the wrong value one exception is a particular implementation of infinitesimal perturbation analysis for which the single run optimization converges to the optimum even with a fixed and small number of ends of service per iteration as a by product of our convergence proofs we obtain some properties of the derivative estimators that could be of independent interest our analysis exploits the regenerative structure of the system but our derivative estimation and optimization algorithms do not always take advantage of that regenerative structure in a companion paper we report numerical experiments with an m m 1 queue which illustrate the basis convergence properties and possible pitfalls of the various techniques

global stochastic optimization with low dispersion point sets this study concerns a generic model free stochastic optimization problem requiring the minimization of a risk function defined on a given bounded domain in a euclidean space smoothness assumptions regarding the risk function are hypothesized and members of the underlying space of probabilities are presumed subject to a large deviation principle however the risk function may well be nonconvex and multimodal a general approach to finding the risk minimizer on the basis of decision observation pairs is proposed it consists of repeatedly observing pairs over a collection of design points principles are derived for choosing the number of these design points on the basis of an observation budget and for allocating the observations between these points in both prescheduled and adaptive settings on the basis of these principles large deviation type bounds of the minimizer in terms of sample size are established

the asymptotic efficiency of simulation estimators a decision theoretic framework is proposed for evaluating the efficiency of simulation estimators the framework includes the cost of obtaining the estimate as well as the cost of acting based on the estimate the cost of obtaining the estimate and the estimate itself are represented as realizations of jointly distributed stochastic processes in this context the efficiency of a simulation estimator based on a given computational budget is defined as the reciprocal of the risk the overall expected cost this framework is appealing philosophically but it is often difficult to apply in practice e g to compare the efficiency of two different estimators because only rarely can the efficiency associated with a given computational budget be calculated however a useful practical framework emerges in a large sample context when we consider the limiting behavior as the computational budget increases a limit theorem established for this model supports and extends a fairly well known efficiency principle

a stochastic quasi newton method for simulation response optimization abstract simulation response optimization has wide applications for management of systems that are so complicated that the performance can only be evaluated by using simulation this paper modifies the quasi newton method used in deterministic optimization to suit the stochastic environment in simulation response optimization the basic idea is to use the estimated subgradient calculated from different replications and a metric matrix updated from the broyden fletcher goldfarb shanno bfgs formula to yield a quasi newton search direction to avoid misjudging the minimal point in both the line search and the quasi newton iterations due to the stochastic nature a t test instead of a simple comparison of the mean responses is performed it is proved that the resulting stochastic quasi newton algorithm is able to generate a sequence that converges to the optimal point under certain conditions empirical results from a four station queueing problem and an s s inventory problem indicate that this method is able to find the optimal solutions in a statistical sense moreover this method is robust with respect to the number of replications conducted at each trial point

backward differentiation type formulas for volterra integral equations of the second kind numerical integration formulas are discussed which are obtained by differentiation of the volterra integral equation and by applying backward differentiation formulas to the resulting integro differential equation in particular the stability of the method is investigated for a class of convolution kernels the accuracy and stability behaviour of the method proposed in this paper is compared with that of i a block implicit runge kutta scheme and ii the scheme obtained by applying directly a quadrature rule which is reducible to the backward differentiation formulas the present method is particularly advantageous in the case of stiff volterra integral equations

gradient based simulation optimization under probability constraints we study optimization problems subject to possible fatal failures the probability of failure should not exceed a given confidence level the distribution of the failure event is assumed unknown but it can be generated via simulation or observation of historical data gradient based simulation optimization methods pose the difficulty of the estimation of the gradient of the probability constraint under no knowledge of the distribution in this work we provide two single path estimators with bias a convolution method and a finite difference and we provide a full analysis of convergence of the arrow hurwicz algorithm which we use as our solver for optimization convergence results are used to tune the parameters of the numerical algorithms in order to achieve best convergence rates and numerical results are included via an example of application in finance

stability of parallel volterra runge kutta methods abstract in this paper we analyse parallel iteration of volterra runge kutta methods pivrk methods for solving second kind volterra integral equations on parallel computers we focus on the determination of the region of convergence c and on the stability region sm of the iterated method obtained after m iterations results are presented for the convolution test equation it turns out that the stability region sm does not necessarily converge to the stability region s of the corrector however for finite m sm need not to be contained in c or s and may be much larger than c

some strong separation in fuzzy topological spaces abstract recently macho stadler et al fuzzy sets and systems 43 1991 95 116 introduced the notion of fuzzy separation using the family of its level topologies lt t t i1 the present work deals with introducing and studying the operations on ri fuzzy topological spaces i 0 1 moreover the notion of fuzzy separation which is well defined as a fuzzy topological concept is described a comparison between the above notions with the analogous fuzzy ones are discussed an acceptable clue which indicates that these notions are equivalent is offered

strong and ultra separation axioms of fuzzy bitopological spaces given a fuzzy bitopological space x 1 2 we introduce a new notion of fuzzy pairwise separation axioms by using the family of its level bitopologies 1 2 0 1 we prove that these concepts are good extension and we compare them with its corresponding fpt kandil and ei shafee 1991 and fpt1 abu safiya et al 1994 i 0 1 2 3 4 respectively we show that these notions are not equivalent and we give a number of examples which illustrate this fact

adaptive step size algorithms for blind interference suppression in ds cdma systems this paper develops adaptive step size blind lms algorithms and adaptive forgetting factor blind rls algorithms for code aided suppression of multiple access interference mai and narrowband interference nbi in ds cdma systems these algorithms optimally adapt both the step size forgetting factor and the weight vector of the blind linear multiuser detector using the received measurements simulations are provided to compare the proposed algorithms with previously studied blind rls and blind lms algorithms they show that the adaptive step size blind lms algorithm and adaptive forgetting factor blind rls algorithm field significant improvements over the standard blind lms algorithm and blind rls algorithm in dynamic environments where the number of interferers are time varying

simulation based optimization with stochastic approximation using common random numbers the method of common random numbers is a technique used to reduce the variance of difference estimates in simulation optimization problems these differences are commonly used to estimate gradients of objective functions as part of the process of determining optimal values for parameters of a simulated system asymptotic results exist which show that using the common random numbers method in the iterative finite difference stochastic approximation optimization algorithm fdsa can increase the optimal rate of convergence of the algorithm from the typical rate of k 1 3 to the faster k 1 2 where k is the algorithm s iteration number simultaneous perturbation stochastic approximation spsa is a newer and often much more efficient optimization algorithm and we will show that this algorithm too converges faster when the common random numbers method is used we will also provide multivariate asymptotic covariance matrices for both the spsa and fdsa errors

discrete time waveform relaxation volterra runge kutta methods convergence analysis the discrete time relaxation methods based on volterra runge kutta methods for solving large system of second kind volterra integral equations are proposed convergence of the discrete time iteration process with particular attention to parallel methods is investigated

stochastic approximation with averaging of the iterates optimal asymptotic rate of convergence for general processes consider the stochastic approximation algorithm x n 1 x n a n g x n xi n in an important paper polyak and juditsky siam j control optim 30 1992 pp 838 855 showed that loosely speaking if the coefficients a n go to zero slower than o 1 n then the averaged sequence sum nolimits i 1 n x i n converged to its limit at an optimum rate for any coefficient sequence the conditions were rather special and direct constructions were used here a rather simple proof is given that results of this type are generic to stochastic approximation and essentially hold any time that the classical asymptotic normality of the normalized and centered iterates holds considerable intuitive insight is provided into the procedure simulations have well borne out the importance of the method

bias properties of budget constrained simulations this paper addresses the bias characteristics of estimators produced from monte carlo simulations if the computer time allocated to the simulation is t then nt the number of replications completed by time t is a renewal process the simulation implications of a known exact expression for the expected value of a sample mean based on nt replications are explored and a similar exact expression for a sample mean based on nt 1 replications is derived bias expansions for a sample mean based on nt or nt 1 replications are obtained the bias in the sample mean based on nt replications is at most of order o1 t under suitable moment conditions the bias decreases at a much faster rate than o1 t on the other hand the estimator based on nt 1 replications has bias of order 1 t the exact expressions also lead to simple and totally unbiased estimators using taylor series the bias expansions of a general function of means based on nt or nt 1 replications are determined the leading terms in these expansions are of order 1 t although the coefficients are different based on these expansions a tin style adjusted estimator is proposed to reduce the bias these expansions are specialized to the case of ratio estimation in regenerative simulation due to a cancellation effect the ratio estimator based on nt 1 cycles is biased only to order o1 t providing confirmation and reinterpretation of a result of m meketon and p heidelberger

a stochastic approximation algorithm with varying bounds many optimization problems that are intractable with conventional approaches will yield to stochastic approximation algorithms this is because these algorithms can be used to optimize functions that cannot be evaluated analytically but have to be estimated for instance through simulation or measured thus stochastic approximation algorithms can be used for optimization in simulation unfortunately the classical stochastic approximation algorithm sometimes diverges because of unboundedness problems we study the convergence of a variant of stochastic approximation defined over a growing sequence of compact sets we show that this variant converges under more general conditions on the objective function than the classical algorithm while maintaining the same asymptotic convergence rate we also present empirical evidence that shows that this algorithm sometimes converges much faster than the classical algorithm

recursive algorithms for estimation of hidden markov models and autoregressive models with markov regime this paper is concerned with recursive algorithms for the estimation of hidden markov models hmms and autoregressive ar models under the markov regime convergence and rate of convergence results are derived acceleration of convergence by averaging of the iterates and the observations are treated finally constant step size tracking algorithms are presented and examined

stability analysis of the de hoog and weiss implicit runge kutta methods for the volterra integral and integrodifferential equations abstract the stability of the de hoog and weiss runge kutta methods is analyzed for the volterra integrodifferential equations with respect to the basic test equation and for volterra integral equations with respect to the linear convolution equation stability regions are determined for some choices of the parameters

generalised filters 1 we continue the study started in 8 of generalised filters prime prefilters have played a central role in the theory of lowen fuzzy uniform spaces and lowen discovered a characterisation of the set of all minimal prime prefilters finer than a given prefilter in terms of ultrafilters we define the notion of a prime generalised filter and describe the set of all minimal prime g filters finer than a given g filter in terms of ultrafilters the relationship between prime prefilters and prime g filters is revealed the behaviour of the images and preimages of g filters are investigated

asymptotic efficiency of perturbation analysis based stochastic approximation with averaging central limit theorems are obtained for the perturbation analysis robbins monro single run parmsr algorithm updated either after every regenerative cycle or after every fixed length observation period and with averaging of the iterates for one dependent regenerative processes when the convergence to the optimizer is expressed in terms of the total observation time of the system or the total computing budget in the case of a simulation the convergence rate and the limit covariance matrix turn out to be the same for all updating schemes and are optimal within the class of stochastic approximation algorithms under certain assumptions a bound on the strong convergence rate of the usual parmsr algorithm updated after every fixed length observation period is established using a limit theorem on double array martingales this is the key step for obtaining central limit theorems for the algorithms with averaging and has interest in its own right

strong separation and strong countability in fuzzy topological spaces given a fuzzy topological space x we introduce new notions of fuzzy separation and fuzzy countability using the family of its level topologies t t 0 1 we check that these are well defined fuzzy topological concepts and we compare them with the analogous fuzzy ones introduced in the literature we verify that these notions are not equivalent and we give a large number of examples which illustrate this fact

highly stable parallel volterra runge kutta methods a new family of parallel v stable methods for second kind volterra integral equations are proposed the methods belong to the class of volterra runge kutta methods and can be applied provided that some not very restrictive conditions on the integral equation kernel are satisfied

parallel algorithm with spectral convergence for nonlinear integro differential equations we discuss a numerical algorithm for solving nonlinear integro differential equations and illustrate our findings for the particular case of volterra type equations the algorithm combines a perturbation approach meant to render a linearized version of the problem and a spectral method where unknown functions are expanded in terms of chebyshev polynomials el gendi s method this approach is shown to be suitable for the calculation of two point green functions required in next to leading order studies of time dependent quantum field theory

the relationship between various filter notions on agl monoid abstract the notion of a generalised filter is extended to the setting of a gl monoid it is shown that there exists a one to one correspondence between the collection of generalised filters on a set x and the collection of strongly stratified l filters on x specialising to the case where l is the closed unit interval 0 c viewed as a heyting algebra we show that any strongly stratified 0 c filter on x can be uniquely identified with a saturated filter on i x with characteristic value c in this way the notion of a generalised filter unifies various filter notions in particular necessity measures and finitely additive probability measures are specific examples of generalised filters

fuzzy convergence structures abstract we define a fuzzy convergence structure which is a correspondence between the prefilters on a given set x and the fuzzy subsets of x the notion of fuzzy convergence structure is shown to be a generalization of a fuzzy topology

some guidelines and guarantees for common random numbers common random numbers crn is a widely used technique for reducing variance in comparing stochastic systems through simulation its popularity derives from its intuitive appeal and ease of implementation however though crn has been observed to work well with a broad range of models the class of systems for which it is provably advantageous has remained rather limited this paper has two purposes we first discuss the effectiveness and optimality of crn in a general setting stressing the roles played by monotonicity and continuity properties we then present specific new classes of systems and comparisons for which crn is beneficial and even optimal our conclusions for these systems are largely consistent with simulation practice and lend further theoretical support to folklore our results differ from those of previous analyses primarily because we put conditions on the timing of events rather than the sequence of states in a discrete event simulation we formulate our results in three settings corresponding to three applications of crn distributional comparisons structural comparisons and sensitivity analysis in each case we make use of conditions that simultaneously ensure monotonicity and continuity in the timing of events these properties are established through explicit recursions for event epochs in terms of increasing continuous functions

stochastic approximation methods for systems over an infinitehorizon the paper develops efficient and general stochastic approximation sa methods for improving the operation of parametrized systems of either the continuous or discrete event dynamical systems types and which are of interest over a long time period for example one might wish to optimize or improve the stationary or average cost per unit time performance by adjusting the systems parameters the number of applications and the associated literature are increasing at a rapid rate this is partly due to the increasing activity in computing pathwise derivatives and adapting them to the average cost problem although the original motivation and the examples come from an interest in the infinite horizon problem the techniques and results are of general applicability in sa we present an updating and review of powerful ordinary differential equation type methods in a fairly general context and based on weak convergence ideas the results and proof techniques are applicable to a wide variety of applications exploiting the full potential of these ideas can greatly simplify and extend much current work their breadth as well as the relative ease of using the basic ideas are illustrated in detail via typical examples drawn from discrete event dynamical systems piecewise deterministic dynamical systems and a stochastic differential equations model in these particular illustrations we use either infinitesimal perturbation analysis type estimators mean square derivative type estimators or finite difference type estimators markov and non markov models are discussed the algorithms for distributed asynchronous updating as well as the fully synchronous schemes are developed

almost sure approximations to the robbins monro and kiefer wolfowitz processes with dependent noise we study a recursive algorithm which includes the multidimensional robbins monro and kiefer wolfowitz processes the assumptions on the disturbances are weaker than the usual assumption that they be a martingale difference sequence it is shown that the algorithm can be represented as a weighted average of the disturbances this representation can be used to prove asymptotic results for stochastic approximation procedures as an example we approximate the one dimensional kiefer wolfowitz process almost surely by brownian motion and as a byproduct obtain a law of the iterated logarithm

on the convergence rates of ipa and fdc derivative estimators we show that under the sufficient conditions usually given for infinitesimal perturbation analysis ipa to apply for derivative estimation a finite difference scheme with common random numbers fdc has the same order of convergence namely o n 1 2 provided that the size of the finite difference interval converges to zero fast enough this holds for both one and two sided fdc this also holds for different variants of ipa such as some versions of smoothed perturbation analysis spa which is based on conditional expectation finally this also holds for the estimation of steady state performance measures by truncated horizon estimators under some ergodicity assumptions our developments do not involve monotonicity but are based on continuity and smoothness we give examples and numerical illustrations which show that the actual difference in mean square error mse between ipa and fdc is typically negligible we also obtain the order of convergence of that difference which is faster than the c

a short note on fuzzy neighbourhood spaces abstract lowen introduced the concept of fuzzy neighbourhood spaces fns s and proved that the family of level topologies of a fns is an antichain wuyts characterized fns s as being those fully stratified fuzzy topological spaces fts s whose level topologies form antichains and whose fuzzy topologies are the finest possible for thier level topologies mashhour et al introduced the axiom of structure a on fts s and derived for it several characterizations and fuzzy topological consequences we use those characterizations of structure a and wuyts characterization of fns s to prove that a fts is a fns iff it is of structure a and fully stratified

uniform type structures on lattice valued spaces and frames by introducing lattice valued covers of a set we present a general framework for uniform structures on very general l valued spaces for l an integral commutative quantale by showing via an intermediate l valued structure of uniformity how filters of covers may describe the uniform operators of hutton we prove that when restricted to girard quantales this general framework captures a significant class of hutton s uniform spaces the categories of l valued uniform spaces and l valued uniform frames here introduced provide in the case l is a complete chain the missing vertices in the commutative cube formed by the classical categories of topological and uniform spaces and their corresponding pointfree counterparts forming the base of the cube and the corresponding l valued categories forming the top of the cube

simulating discounted costs we numerically estimate via simulation the expected infinite horizon discounted cost d of running a stochastic system a naive strategy estimates a finite horizon approximation to d we propose alternatives all are ranked with respect to asymptotic variance as a function of computer time budget and discount rate when semi markov and or regenerative structure or neither is assumed in this setting the naive truncation estimator loses it may triumph however when the computer time budget is modest the discount rate is large and the process simulated is not regenerative or has long cycle lengths

acceleration of stochastic approximation by averaging a new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated convergence with probability one is proved for a variety of classical optimization and identification problems it is also demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence

on fuzzy bitopological spaces abstract in this paper we have used the fuzzy topologies 1 and 2 to generate a family s which is a supra fuzzy topology on x using the family s we introduce and study the concepts of separation axioms continuity resp openness closedness of a mapping and compactness for a fuzzy bitopological space x 1 2 our definitions preserve much of the correspondence between concepts of fuzzy bitopological spaces and the associated fuzzy topological spaces we then investigate the relationship between these concepts and their correspondence with the fuzzy bitopological spaces kandil and el shafee 1991

budget dependent convergence rate of stochastic approximation convergence rate results are derived for a stochastic optimization problem where a performance measure is minimized with respect to a vector parameter t assuming that a gradient estimator is available and that both the bias and the variance of the estimator are known functions of the budget devoted to its computation the gradient estimator is employed in conjunction with a stochastic approximation sa algorithm our interest is to figure out how to allocate the total available computational budget to the successive sa iterations the effort is devoted to solving the asymptotic version of this problem by finding the convergence rate of sa toward the optimizer first as a function of the number of iterations and then as a function of the total computational effort as a result the optimal rate of increase of the computational budget per iteration can be found explicit expressions for the case where the computational budget devoted to an iteration is a polynomial in the iteration number and where the bias and variance of the gradient estimator are polynomials of the computational budget are derived applications include the optimization of steady state simulation models with likelihood ratio perturbation analysis or finite difference gradient estimators optimization of infinite horizon models with discounting optimization of functions of several expectations and so on several examples are discussed our results readily generalize to general root finding problems

on n convergence of fuzzy nets abstract in this paper we define the n convergence of fuzzy nets in a fuzzy topological space and we use it to give a characterization of some fuzzy topological concepts we give necessary conditions for the n convergence of fuzzy nets in a fuzzy topological space and we characterize this n convergence in a topologically generated fuzzy topological space we also study some characterizations of fuzzy ultranets and we introduce the concept of subordination between fuzzy nets we associate to each fuzzy net in x a prefilter on x and conversely and we give an exhaustive description of the connections between these two theories we give a theory of fuzzy convergence classes and we characterize fuzzy topologies via some special types of fuzzy convergence classes

stochastic optimization by simulation numerical experiments with the m m 1 queue in steady state this paper gives numerical illustrations of the behavior of stochastic approximation combined with different derivative estimation techniques to optimize a steady state system it is a companion paper to l ecuyer and glynn 1993 which gives convergence proofs for most of the variants experimented here the numerical experiments are made with a simple m m 1 queue which while simple serves to illustrate the basic convergence properties and possible pitfalls of the various techniques

characterization of the probabilistic traveling salesman problem we show that stochastic annealing can be successfully applied to gain new results on the probabilistic traveling salesman problem the probabilistic traveling salesman must decide on an a priori order in which to visit n cities randomly distributed over a unit square before learning that some cities can be omitted we find the optimized average length of the pruned tour follows e l over bar pruned rootnp 0 872 0 105p f np where p is the probability of a city needing to be visited and f np 1 as np infinity the average length of the a priori tour before omitting any cities is found to follow e l a priori rootn pbeta p where beta p 1 1 25 0 82 ln p is measured for 0 05less than or equal topless than or equal to0 6 scaling arguments and indirect measurements suggest that beta p tends towards a constant for p 0 03 our stochastic annealing algorithm is based on limited sampling of the pruned tour lengths exploiting the sampling error to provide the analog of thermal fluctuations in simulated thermal annealing the method has general application to the optimization of functions whose cost to evaluate rises with the precision required

strong and ultra separation axioms on l fuzzy topological spaces given an l fuzzy topological space x d we introduce new notions of l fuzzy separation axioms using the family of its level topology i a d a pr l we check that these are well defined l fuzzy topological concepts and we compare them with the analogous l fuzzy ones introduced in the literature we verify that these notations are not equivalent and we give many examples which illustrate this fact furthermore some results concerning the new concepts have been established

almost sure convergence of stochastic approximation algorithms with non additive noise abstract stochastic approximation algorithms with non additive noise are discussed in studying strong convergence of such algorithms traditionally one assumes that the iterates return to a bounded or compact set infinitely often or that the function under consideration grows with certain rate the usual projection algorithms require that the bounded projection region is known beforehand it is desirable to weaken these boundedness conditions by introducing randomly varying truncations chen and zhu 1986 achieved this for stochastic approximation algorithms with additive noise here we extend their result to a more general setting