generalized vector version of minty s lemma and applications abstract in this paper we consider a generalized vector version of minty s lemma and then show the existence of solutions to generalized vector variational type inequality problems for set valued mappings as an application

a remark on a standard and linear vector network equilibrium problem with capacity constraints in this paper weak vector equilibrium principle with capacity constraints is introduced a necessary condition that a vector minimum cost flow is a vector equilibrium flow with capacity constraints is obtained when the number of paths connecting with each pair of source and sink is less than or equal to 2 a sufficient condition for a vector minimum cost flow to be a vector equilibrium flow is also obtained a generalized weak vector equilibrium principle is also introduced without any additional assumption a necessary and sufficient condition for a weak vector minimum cost flow to be a generalized weak vector equilibrium flow is obtained

approximation algorithms for np complete problems on planar graphs this paper describes a general technique that can be used to obtain approximation schemes for various np complete problems on planar graphs the strategy depends on decompos ing a planar graph into subgraphs of a form we call k outerplanar for fixed k the problems of interest are solvable optimally in linear time on k outerplanar graphs by dynamic programming for general planar graphs if the problem is a maximization problem such as maximum independent set this technique gives for each k a linear time algorithm that produces a solution whose size is at least k k 1 optimal if the problem is a minimization problem such as minimum vertex cover it gives for each k a linear time algorithm that produces a solution whose size is at most k 1 k optimal taking k c log log nl or k c log nl where n is the number of nodes and c is some constant we get polynomial time approximation algorithms whose solution sizes converge toward optimal as n increases the class of problems for which this approach provides approximation schemes includes maximum independent set maximum tile salvage partition into triangles maximum h matching minimum vertex cover minimum dominat ing set and minimum edge dominating set for these and certain other problems the proof of solvability on k outerplanar graphs also enlarges the class of planar gmphs for which the problems are known to be solvable in polynomial time

on the generalized vector equilibrium problems in this paper generalized vector equilibrium problems are studied and some existence theorems of solutions for these problems in the setting of topological vector spaces are proved sufficient conditions for the set of solutions to be compact and convex are given our results improve some recent results in this field

universal detection of messages via finite state channels we propose a universal asymptotically optimum decision rule for deciding whether or not an observed sequence generated at the output of an unknown finite state channel corresponds to a given channel input message the hypothesized message is tested against a certain alternative message or several alternative messages under the neyman pearson criterion

application of kolmogorov complexity and universal codes to identity testing and nonparametric testing of serial independence for time series we show that kolmogorov complexity and such its estimators as universal codes or data compression methods can be applied for hypotheses testing in a framework of classical mathematical statistics the methods for identity testing and nonparametric testing of serial independence for time series are suggested

absolute optimal solution for a compact and convex game abstract this paper investigates the existence of absolute optimal solutions for a partition p in continuous and quasiconcave games we show that the p consistency property introduced in the paper together with the quasiconcavity and continuity of payoffs permits the existence of p absolute optimal solutions in games with compact and convex strategy spaces the p consistency property is a general condition that cannot be dispensed with for the existence of p absolute optimal solutions we also characterize the existence of p absolute optimal solutions by providing necessary and sufficient conditions moreover we suggest an algorithm for efficiently computing p absolute optimal solutions

decomposition of generalized vector variational inequalities abstract a multicriteria optimization problem is called pareto reducible if its weakly efficient solutions actually are efficient solutions for the problem itself or for at least one subproblem obtained from it by selecting certain criteria the aim of this paper is to investigate a similar property within a special class of generalized vector variational inequalities under appropriate generalized convexity assumptions

an equivalent markov model for burst errors in digital channels a hidden markov model for burst errors is specified by a probability transition matrix p an initial probability vector p and the state dependent probability of error matrix b several procedures are available for estimating p p and b from a given error observation sequence however even with some restrictions on the structure of the underlying markov models the estimation procedures are computationally intensive particularly when the observation sequence contains long strings of identical symbols we show that under some mild assumptions a markov model with an arbitrary transition matrix p is equivalent to a markov model with a unique block diagonal transition matrix spl lambda we also present a computationally very efficient algorithm for estimating spl lambda from a set of observation using a modified baum welch 1972 algorithm

existence of solutions for vector optimization problems we define the generalized efficient solution which is more general than the weakly efficient solution for vector optimization problems and prove the existence of the generalized efficient solution for nondifferentiable vector optimization problems by using vector variational like inequalities for set valued maps

several extensions of the abian brown fixed point theorem and their applications to extended and generalized nash equilibria on chain complete posets abstract in this paper we provide several extensions of the abian brown fixed point theorem from single valued mappings to set valued mappings on chain complete posets then we examine some non monetized non cooperative games where both the collections of the strategies and the ranges of the utilities for the players are posets by applying the extensions of the abian brown fixed point theorem and by applying the order preserving property of mappings we prove some existence theorems of extended and generalized nash equilibria for non monetized non cooperative games on chain complete posets

a multicriteria pareto optimal path algorithm abstract in this paper we present an algorithm for finding in a multicriteria network pareto optimal paths one each for each efficient objective vector validation of the algorithm and two illustrative examples are included computational experience is also reported this algorithm is a generalization of an earlier one for the bicriterion case

an on line universal lossy data compression algorithm via continuous codebook refinement ii optimality for phi mixing source models for pt i see ibid vol 42 no 3 p 803 21 1996 two versions of the gold washing data compression algorithm one with codebook innovation interval and the other with finitely many codebook innovations are considered the version of the gold washing algorithm with codebook innovation interval k is a variant of the gold washing algorithm such that the codebook is innovated once every k 1 source words during the process of encoding the entire source it is demonstrated that when this version of the gold washing algorithm is applied to encode a stationary spl phi mixing source the expected distortion performance converges to the distortion rate function of the source as the codebook length goes to infinity furthermore if the source to be encoded is a markov source or a finite state source then the corresponding sample distortion performance converges almost surely to the distortion rate function the version of the gold washing algorithm with finitely many codebook innovations is a variant of the gold washing algorithm in which after finitely many codebook innovations the codebook is held fixed and reused to encode the forthcoming source sequence block by block similar results are shown for this version of the gold washing algorithm in addition the convergence speed of the algorithm is discussed

sensitivity analysis of parametric weak vector equilibrium problems in this paper two implicit multifunction theorems are obtained then by using a set valued gap function and the results obtained we study the sensitivity analysis of the solution mapping for a parametric weak vector equilibrium problem and obtain an explicit expression for the contingent derivative of the solution mapping

on the estimation of the order of a markov chain and universal data compression the authors estimate the order of a finite markov source based on empirically observed statistics the performance criterion adopted is to minimize the probability of underestimating the model order while keeping the overestimation probability exponent at a prescribed level a universal asymptotically optimal test in the sense just defined is proposed for the case where a given integer is known to be the upper bound of the true order for the case where such a bound is unavailable an alternative rule based on the lempel ziv data compression algorithm is shown to be asymptotically optimal also and computationally more efficient

feasibility and solvability of vector variational inequalities with moving cones in banach spaces abstract in this paper we study the feasibility and solvability of vector variational inequalities with moving cones in banach spaces we show that the strict feasibility implies solvability of vector variational inequalities with moving cones under suitable conditions further we show that under suitable conditions the homogeneous vector variational inequality with a moving cone is solvable whenever it is feasible as consequences we obtain the solvability of vector variational inequalities with feasibility assumptions in banach spaces

second order contingent derivatives of set valued mappings with application to set valued optimization abstract in this paper a family of parameterized set valued optimization problems whose constraint set depends on a parameter are considered some calculus rules are obtained for calculating the second order contingent derivatives of the composition and sum of two set valued mappings then by using these calculus rules some results concerning second order sensitivity analysis are established and an explicit expression for the second order contingent derivative of the weak perturbation mapping in the set valued optimization problems is obtained

vector equilibrium problem and vector optimization this paper examines the vector equilibrium model based on a vector cost consideration this is a generalization of the well known wardrop traffic equilibrium principle where road users choose paths based on just a single cost the concept of parametric equilibria is introduced and used to establish relations with parametric complementarity and variational inequality problems relations with some vector optimization problems via scalarization techniques are given under appropriate conditions some solution methods for solving vector equilibrium problems are also discussed

on generalized vector pre variational and pre quasivariational inequalities in this paper we consider generalized vector pre variational inequality problems as well as vector pre quasivariational inequality problems in abstract space setting we establish several existence results for these two classes of problems by employing the ky fan lemma and a scalarization technique respectively

estimating the number of states of a finite state source the problem of estimating the number of states of a finite alphabet finite state source is investigated an estimator is developed that asymptotically attains the minimum probability of understanding the number of states among all estimators with a prescribed exponential decay rate of overestimation probability the proposed estimator relies on the lempel ziv data compression algorithm in an intuitively appealing manner

universal classification for hidden markov models binary hypotheses testing using empirically observed statistics is studied in the neyman pearson formulation for the hidden markov model hmm an asymptotically optimal decision rule is proposed and compared to the generalized likelihood ratio test glrt which has been shown in earlier studies to be asymptotically optimal for simpler parametric families the proof of the main theorem is provided the result can be applied to several types of hmms commonly used in speech recognition and communication applications several applications are demonstrated

weak sharp solutions of variational inequalities xuexiang huang pointed out that the statement on line 5 of page 184 of p marcotte and d zhu siam j optim 9 1999 pp 179 189 is invalid and supplied an alternative proof of the inequality that appears on line 10 here is a simple proof of this result due to an anonymous referee the substitution starts at line 4 and ends at line 11

non cooperative facility location and covering games we consider a general class of non cooperative games related to combinatorial covering and facility location problems a game is based on an integer programming formulation of the corresponding optimization problem and each of the k players wants to satisfy a subset of the constraints for that purpose resources available in integer units must be bought and their cost can be shared arbitrarily between players we consider the existence and cost of exact and approximate pure strategy nash equilibria in general the prices of anarchy and stability are in q k and deciding the existence of a pure nash equilibrium is np hard under certain conditions however cheap nash equilibria exist in particular if the integrality gap of the underlying integer program is 1 or in the case of single constraint players we also present algorithms that compute simultaneously near stable and near optimal approximate nash equilibria in polynomial time

vector variational inequality as a tool for studying vector optimization problems the paper aims to show that a vector variational inequality can be an useful tool for studying a vector optimization problem

sensitivity analysis in variational inequalities in this paper we derive conditions for the local uniqueness continuity and differentiability of a solution of parametric variational inequalities our approach is new and has a strong geometric flavor as an illustration we discuss the sensitivity of the classical complementarity problem

strongly consistent code based identification and order estimation for constrained finite state model classes observations are made of data generated by a stationary ergodic finite alphabet information source according to an unknown statistical model two modeling problems the identification problem and the order estimation problem are considered it is required that the given model class in the identification problem and each given model class in the order estimation problem be a constrained finite state model class which is a type that includes many model classes of information theoretic interest strongly consistent decision rules are exhibited in both the identification problem and the order estimation problem the decision rules are code based in that a model class is chosen based on how well a certain code for that class encodes the observed data the code used for a model class is based on the maximum likelihood code for that class and asymptotic code performance is gauged by means of a key property of divergence rate distance

generalized vector quasi equilibrium problems with applications in this paper we consider the generalized vector quasi equilibrium problem with or without involving condensing maps and prove the existence of its solution by using known fixed point and maximal element theorems as applications of our results we derive some existence results for a solution to the vector quasi optimization problem for nondifferentiable functions and vector quasi saddle point problem

weak sharpness for gap functions in vector variational inequalities abstract in this paper characterizations of the set of solutions for vvi are presented by using scalarization approaches the set of solutions of vvi is shown to be the set of weak sharpness for gap functions of some scalarization of vvi and for gap functions of vvi under semi strong monotonicity some examples are given to illustrate these results

on strong consistency of model selection in classification this paper considers model selection in classification in many applications such as pattern recognition probabilistic inference using a bayesian network prediction of the next in a sequence based on a markov chain the conditional probability p y y x x of class yisiny given attribute value xisinx is utilized by model we mean the equivalence relation in x for x x isinxx x harrp y y x x p y y x x forall yisiny by classification we mean the number of such equivalence classes is finite we estimate the model from n samples zn xi yi i 1 n isin xtimesy n using information criteria in the form empirical entropy h plus penalty term k 2 dn the model such that h k 2 dn is minimized is the estimated model where k is the number of independent parameters in the model and dn n 1 infin is a real nonnegative sequence such that lim supndn n 0 for autoregressive processes although the definitions of h and k are different it is known that the estimated model almost surely coincides with the true model as nrarrinfin if dn n 1 infin 2loglogn n 1 infin and that it does not if dn n 1 infin 2loglogn n 1 infin hannan and quinn the problem whether the same property is true for classification was open this paper solves the problem in the affirmative

the generalized vector quasi variational like inequalities abstract in this paper we introduce and study a class of generalized vector quasi variational like inequality problem gvqvlip involving set valued mappings with certain monotonicity by employing the scalarization technique several existence results for solutions of the gvqvlip are established under noncompact setting in topological vector spaces these new existence results improve unify and generalize many known results for scalar and vector variational inequalities in recent literature

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

greedy facility location algorithms analyzed using dual fitting with factor revealing lp in this article we will formalize the method of dual fitting and the idea of factor revealing lp this combination is used to design and analyze two greedy algorithms for the metric uncapacitated facility location problem their approximation factors are 1 861 and 1 61 with running times of o m log m and o n3 respectively where n is the total number of vertices and m is the number of edges in the underlying complete bipartite graph between cities and facilities the algorithms are used to improve recent results for several variants of the problem

on generalized operator quasi equilibrium problems abstract in this paper we will introduce the generalized operator equilibrium problem and generalized operator quasi equilibrium problem which generalize the operator equilibrium problem due to kazmi and raouf k r kazmi a raouf a class of operator equilibrium problems j math anal appl 308 2005 554 564 into multi valued and quasi equilibrium problems using a fan browder type fixed point theorem in s park foundations of the kkm theory via coincidences of composites of upper semicontinuous maps j korean math soc 31 1994 493 519 and an existence theorem of equilibrium for 1 person game in x p ding w k kim k k tan equilibria of non compact generalized games with l majorized preferences j math anal appl 164 1992 508 517 as basic tools we prove new existence theorems on generalized operator equilibrium problem and generalized operator quasi equilibrium problem which includes operator equilibrium problems

differential and sensitivity properties of gap functions for minty vector variational inequalities the purpose of this paper is to investigate differential properties of a class of set valued maps and gap functions involving minty vector variational inequalities relationships between their contingent derivatives are discussed an explicit expression of the contingent derivative for the class of set valued maps is established optimality conditions of solutions for minty vector variational inequalities are obtained

optimal error exponents in hidden markov models order estimation we consider the estimation of the number of hidden states the order of a discrete time finite alphabet hidden markov model hmm the estimators we investigate are related to code based order estimators penalized maximum likelihood ml estimators and penalized versions of the mixture estimator introduced by liu and narayan 1994 we prove strong consistency of those estimators without assuming any a priori upper bound on the order and smaller penalties than previous works we prove a version of stein s lemma for hmm order estimation and derive an upper bound on underestimation exponents then we prove that this upper bound can be achieved by the penalized ml estimator and by the penalized mixture estimator the proof of the latter result gets around the elusive nature of the ml in hmm by resorting to large deviation techniques for empirical processes finally we prove that for any consistent hmm order estimator for most hmm the overestimation exponent is null

optimality conditions for vector equilibrium problems in this paper we present the necessary and sufficient conditions for weakly efficient solution henig efficient solution globally efficient solution and superefficient solution to the vector equilibrium problems with constraints as applications we give the necessary and sufficient conditions for corresponding solution to the vector variational inequalities and vector optimization problems

remarks on relations between vector variational inequality and vector optimization problem in this paper we study equivalent relations between vector variational inequalities for subdifferentials and nondifferentiable convex vector optimization problems futhermore using the equivalent relations we give existence theorems for solutions of convex vector optimization problems

error exponents for ar order testing this paper is concerned with error exponents in testing problems raised by autoregressive ar modeling the tests to be considered are variants of generalized likelihood ratio testing corresponding to traditional approaches to autoregressive moving average arma modeling estimation in several related problems such as markov order or hidden markov model order estimation optimal error exponents have been determined thanks to large deviations theory ar order testing is specially challenging since the natural tests rely on quadratic forms of gaussian processes in sharp contrast with empirical measures of markov chains the large deviation principles ldps satisfied by gaussian quadratic forms do not always admit an information theoretic representation despite this impediment we prove the existence of nontrivial error exponents for gaussian ar order testing and furthermore we exhibit situations where the exponents are optimal these results are obtained by showing that the log likelihood process indexed by ar models of a given order satisfy an ldp upper bound with a weakened information theoretic representation

stability and sensitivity analysis in convex vector optimization in this paper stability and sensitivity of the efficient set in convex vector optimization are considered the perturbation map is defined as a set valued map it associates with each parameter vector the set of all minimal points of the parametrized feasible set with respect to an ordering cone in the objective space sufficient conditions for the upper and lower semicontinuity of the perturbation map are obtained because of the convexity assumptions the conditions obtained are fairly simple if compared to those in the general case moreover a complete characterization of the contingent derivative of the perturbation map is obtained under some assumptions it provides quantitative information on the behavior of the perturbation map

existence of vector mixed variational inequalities in banach spaces abstract the purpose of this paper is to study the solvability for vector mixed variational inequalities for short vmvi in banach spaces utilizing ky fan s lemma and nadler s theorem we derive the solvability for vmvis with compositely monotone vector multifunctions on the other hand we first introduce the concepts of compositely complete semicontinuity and compositely strong semicontinuity for vector multifunctions then we prove the solvability for vmvis without monotonicity assumption by using these concepts and by applying brouwer s fixed point theorem the results presented in this paper are extensions and improvements of some earlier and recent results in the literature

a sequential algorithm for the universal coding of finite memory sources the estimation and universal compression of discrete sources are considered and a sequential algorithm for the universal coding of finite memory sources attaining asymptotically minimum redundancy is presented the algorithm performs an online estimation of the source states and uses an arithmetic code

mechanism design for set cover games with selfish element agents in this article we study the set cover games when the elements are selfish agents each of which has a privately known valuation of receiving the service from the sets i e being covered by some set each set is assumed to have a fixed cost we develop several approximately efficient strategyproof mechanisms that decide after soliciting the declared bids by all elements which elements will be covered which sets will provide the coverage to these selected elements and how much each element will be charged for single cover set cover games we present a mechanism that is at least 1d m a x efficient i e the total valuation of all selected elements is at least 1d m a x fraction of the total valuation produced by any mechanism here d m a x is the maximum size of the sets for multi cover set cover games we present a budget balanced strategyproof mechanism that is 1d m a xh d m a x efficient under reasonable assumptions here h n is the harmonic function for the set cover games when both sets and elements are selfish agents we show that a cross monotonic payment sharing scheme does not necessarily induce a strategyproof mechanism

a generalized vector variational inequality problem with a set valued semi monotone mapping abstract in this paper we first generalize the concept of semi monotonicity for a scalar single valued mapping to the case of a vector set valued mapping then we consider a generalized vector variational inequality problem concerning the vector set valued semi monotone mapping several existence results are obtained by using the kakutani fan glicksberg fixed point theorem which generalize some results for vector variational inequality problems studied in recent years

on universal types the universal type class of a sequence xn is defined in analogy to the notion underlying the classical method of types two sequences of the same length are said to be of the same universal lz type if and only if they yield the same dictionary or equivalently parsing tree in the incremental parsing of ziv and lempel 1978 it is shown that for any finite order k the variational distance between the kth order empirical probability distributions of two sequences of the same universal type vanishes as the sequence length tends to infinity consequently for any k and any kth order probability assignment the difference between the normalized logarithms of the probabilities assigned to two sequences of the same universal type also vanishes asymptotically the size of a universal type class is studied and it is shown that its asymptotic behavior parallels that of the conventional counterpart with the lz78 code length playing the role of the empirical entropy the number of universal types for sequences of length n is estimated and shown to be of the form exp 1 o 1 gamman logn for a well characterized constant gamma algorithms for enumerating the sequences in a universal type class and for drawing a sequence from the class with uniform probability are described as an application the problem of universal simulation of individual sequences is considered a sequence drawn with uniform probability from the universal type class of xn is an optimal simulation of xn in a well defined mathematical sense

universal filtering via hidden markov modeling the problem of discrete universal filtering in which the components of a discrete signal emitted by an unknown source and corrupted by a known discrete memoryless channel dmc are to be causally estimated is considered a family of filters are derived and are shown to be universally asymptotically optimal in the sense of achieving the optimum filtering performance when the clean signal is stationary ergodic and satisfies an additional mild positivity condition our schemes are comprised of approximating the noisy signal using a hidden markov process hmp via maximum likelihood ml estimation followed by the use of the forward recursions for hmp state estimation it is shown that as the data length increases and as the number of states in the hmp approximation increases our family of filters attains the performance of the optimal distribution dependent filter an extension to the case of channels with memory is also established

analytic efficient solution set for multi criteria quadratic programs abstract we present active set methods to evaluate the exact analytic efficient solution set for multi criteria convex quadratic programming problems mcqp subject to linear constraints the idea is based on the observations that a strictly convex programming problem admits a unique solution and that the efficient solution set for a multi criteria strictly convex quadratic programming problem with linear equality constraints can be parameterized the case of bi criteria quadratic programming bcqp is first discussed since many of the underlying ideas can be explained much more clearly in the case of two objectives in particular we note that the efficient solution set of a bcqp problem is a curve on the surface of a polytope the extension to problems with more than two objectives is straightforward albeit some slightly more complicated notation two numerical examples are given to illustrate the proposed methods

iterative methods for variational and complementarity problems in this paper we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems included among such methods are the newton and several successive overrelaxation algorithms for the most part the study is concerned with the family of linear approximation methods these are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches the paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria finally several convergence results are obtained for some nonlinear approximation methods

on the generalized vector variational inequality problem abstract in this paper we study vector variational inequalities with set valued mappings the concept of c x pseudomonotone mapping is introduced by employing the fan lemma we establish several existence results the new results extend and unify existence results of vector variational inequalities for single valued operators under the banach space setting

on the connectedness of the solution set for the weak vector variational inequality the main aim of this paper is to provide a sufficient condition which guarantees the connected property of the solution set for a kind of weak vector variational inequality

holder continuity of perturbed solution set for convex optimization problems abstract in this paper we first establish sufficient conditions for the local uniqueness and holder continuity of perturbed solution set for a scalar optimization problem then by using a linear scalarization method we obtain the holder continuity of two classes of perturbed solution sets for a multiobjective programming problem respectively we also give some examples to illustrate that our main results are applicable these examples are also given to illustrate that our main results are new and different from the ones in literature

existence and duality of generalized vector equilibrium problems abstract in this paper we propose some dual formulations of generalized vector equilibrium problems by using such dual formulations we prove the existence of a solution to the generalized vector equilibrium problem under generalized pseudomonotonicity conditions the results of this paper extend and generalize the results of i v konnov and s schaible 2000 j optim theory appl 104 395 408

algorithmic aspects of the core of combinatorial optimization games we discuss an integer programming formulation for a class of cooperative games we focus on algorithmic aspects of the core one of the most important solution concepts in cooperative game theory central to our study is a simple but very useful observation that the core for this class is nonempty if and only if an associated linear program has an integer optimal solution based on this we study the computational complexity and algorithms to answer important questions about the cores of various games on graphs such as maximum flow connectivity maximum matching minimum vertex cover minimum edge cover maximum independent set and minimum coloring

order estimation for a special class of hidden markov sources and binary renewal processes we consider the estimation of the order i e the number of hidden states of a special class of discrete time finite alphabet hidden markov sources this class can be characterized in terms of equivalent renewal processes no a priori bound is assumed on the maximum permissible order an order estimator based on renewal types is constructed and is shown to be strongly consistent by computing the precise asymptotics of the probability of estimation error the probability of underestimation of the true order decays exponentially in the number of observations while the probability of overestimation goes to zero sufficiently fast it is further shown that this estimator has the best possible error exponent in a large class of estimators our results are also valid for the general class of binary independent renewal processes with finite mean renewal times

universal coding with minimum probability of codeword length overflow lossless block to variable length source coding is studied for finite state finite alphabet sources the aim is to minimize the probability that the normalized length of the codeword will exceed a given threshold b subject to the kraft inequality it is shown that the lempel ziv algorithm 1978 asymptotically attains the optimal performance in the sense just defined independently of the source and the value of b for the subclass of unifilar markov sources faster convergence to the asymptotic optimum performance can be accomplished by using the minimum description length universal code for this subclass it is demonstrated that these universal codes are also nearly optimal in the sense of minimizing buffer overflow probability and asymptotically optimal in a competitive sense

on the value of coordination in network design we study network design games where n self interested agents have to form a network by purchasing links from a given set of edges we consider shapley cost sharing mechanisms that split the cost of an edge in a fair manner among the agents using the edge it is well known that the price of anarchy of these games is as high as n another line of research has focused on evaluating the price of stability i e the cost of the best nash equilibrium relative to the social optimum in this paper we investigate to which extent coordination among agents can improve the quality of solutions we resort to the concept of strong nash equilibria which were introduced by aumann and are resilient to deviations by coalitions of agents we analyze the price of anarchy of strong nash equilibria and develop lower and upper bounds for unweighted and weighted games in both directed and undirected graphs these bounds are tight or nearly tight for many scenarios it shows that by using coordination the price of anarchy drops from linear to logarithmic bounds we complement these results by also proving the first superconstant lower bound on the price of stability of standard equilibria without coordination in undirected graphs more specifically we show a lower bound of omega log w log log w for weighted games where w is the total weight of all the agents this almost matches the known upper bound of o log w our results imply that for most settings the worst case performance ratios of strong coordinated equilibria are essentially always as good as the performance ratios of the best equilibria achievable without coordination these settings include unweighted games in directed graphs as well as weighted games in both directed and undirected graphs

on generalized vector variational like inequalities abstract in this paper we consider a vector version of minty s lemma and obtain existence theorems for two kinds of variational like inequality a fixed point theorem is also discussed

equilibrium problems with set valued mappings in banach spaces abstract in this paper we consider two classes of equilibrium problems which imply general pseudomonotonicity and general semipseudomonotonicity relative to a set valued map on reflexive and nonreflexive banach spaces respectively using the classical kkm technique we obtain some existence results under boundedness as well as under unboundedness assumptions some examples are given

vector variational like inequalities with generalized bifunctions defined on nonconvex sets abstract in this paper the nonemptiness and compactness of solution sets for stampacchia vector variational like inequalities for short svvlis and minty vector variational like inequalities for short mvvlis with generalized bifunctions defined on nonconvex sets are investigated by introducing the concepts of generalized weak cone pseudomonotonicity and generalized proper cone suboddness moreover some equivalent relations between a solution of svvlis and mvvlis and a generalized weakly efficient solution of vector optimization problems for short vops are established under the assumptions of generalized pseudoconvexity and generalized invexity in the sense of clarke generalized directional derivative these results extend and improve the corresponding results of others

the minimum description length principle in coding and modeling we review the principles of minimum description length and stochastic complexity as used in data compression and statistical modeling stochastic complexity is formulated as the solution to optimum universal coding problems extending shannon s basic source coding theorem the normalized maximized likelihood mixture and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms we assess the performance of the minimum description length criterion both from the vantage point of quality of data compression and accuracy of statistical inference context tree modeling density estimation and model selection in gaussian linear regression serve as examples

optimal watermark embedding and detection strategies under limited detection resources an information theoretic approach is proposed to watermark embedding and detection under limited detector resources first the attack free scenario is considered under which asymptotically optimal decision regions in the neyman pearson sense are proposed along with the optimal embedding rule later the case of zero mean independent and identically distributed i i d gaussian covertext distribution is explored with unknown variance under the attack free scenario for this case a lower bound on the exponential decay rate of the false negative probability is proposed it is proven that the optimal embedding and detecting strategy is superior to the customary linear additive embedding strategy in the exponential sense finally these results are extended to the case of memoryless attacks and general worst case attacks optimal decision regions and embedding rules are offered and the worst attack channel is identified

order estimation and sequential universal data compression of a hidden markov source by the method of mixtures we consider first the estimation of the order i e the number of states of a discrete time finite alphabet stationary ergodic hidden markov source hms our estimator uses a description of the observed data in terms of a uniquely decodable code with respect to a mixture distribution obtained by suitably mixing a parametric family of distributions on the observation space this procedure avoids maximum likelihood calculations the order estimator is shown to be strongly consistent with the probability of underestimation decaying exponentially fast in the number n of observations while the probability of overestimation does not exceed cn sup 3 where c is a constant next we present a sequential algorithm for the uniquely decodable universal data compression of the hms which performs an on line estimation of source order followed by arithmetic coding this code asymptotically attains optimum average redundancy

on solution sets for affine vector variational inequality abstract in this paper we discuss the boundedness and connectedness of solution sets for affine vector variational inequalities with noncompact polyhedral constraint sets and positive semidefinite or monotone matrices moreover we show that the boundedness and connectedness result can be applied to a multiobjective linear fractional optimization problem and a multiobjective convex linear quadratic optimization problem

strong and weak convexity of sets and functions in this paper we study two classes of sets strongly and weakly convex sets for each class we derive a series of properties which involve either the concept of supporting ball an obvious extension of the concept of supporting hyperplane or the normal cone to the set we also study a class of functions denoted convex which satisfy for arbitrary points x1 and x2 and any value 0 1 the classical inequality of convex functions up to a term 1 x1 x2 2 depending on the sign of the constant the function is said to be strongly or weakly convex we provide characteristic properties of this class of sets and we relate it to strongly and weakly convex sets via the epigraph and the level sets finally we give three applications a separation theorem a sufficient condition for global optimum of a nonconvex programming problem and a sufficient geometrical condition for a set to be a manifold

on implicit vector equilibrium problems in this paper we introduce and study a class of implicit vector equilibrium problems which includes a number of scalar implicit equilibrium problems implicit variational inequalities and implicit complementarity problems as special cases by using kkm fan theorem we prove some new existence theorems of solutions for this kind of implicit vector equilibrium problems in hausdorff topological vector spaces our results extend and unify some corresponding results of several authors

strong vector f complementary problem and least element problem of feasible set abstract in this paper we introduce several classes of strong vector f complementary problems and give some existence results for these problems in banach spaces we also discuss the least element problems of feasible sets and present their relations with the strong vector f complementary problems

the online median problem we introduce a natural variant of the metric uncapacitated k median problem that we call the online median problem whereas the k median problem involves optimizing the simultaneous placement of k facilities the online median problem imposes the following additional constraints the facilities are placed one at a time a facility cannot be moved once it is placed and the total number of facilities to be placed k is not known in advance the objective of an online median algorithm is to minimize the competitive ratio that is the worst case ratio of the cost of an online placement to that of an optimal offline placement our main result is a constant competitive algorithm for the online median problem running in time that is linear in the input size in addition we present a related though substantially simpler constant factor approximation algorithm for the metric uncapacitated facility location problem that runs in time linear in the input size the latter algorithm is similar in spirit to the recent primal dual based facility location algorithm of jain and vazirani but our approach is more elementary and yields an improved running time while our primary focus is on problems which ask us to minimize the weighted average service distance to facilities we also show that our results can be generalized to hold to within constant factors for more general objective functions for example we show that all of our approximation results hold to within constant factors for the k means objective function

on existence of vector equilibrium flows with capacity constraints of arcs in this paper we propose a weak vector equilibrium principle with capacity constraints of arcs by proving the existence of solutions for the weighted variational inequality we establish the existence results of weak vector traffic equilibrium flows with capacity constraints of arcs

existence of solutions for generalized variational inequality problems in banach spaces abstract in this paper we prove the existence of solutions of generalized variational inequality for upper semicontinuous multivalued mappings with compact contractible values over compact convex subsets in a reflexive banach space with a frechet differentiable norm moreover we give some conditions that guarantee the existence of solutions of generalized variational inequality for upper semicontinuous multivalued mappings with compact contractible values over unbounded closed convex subsets the result obtained in this paper improves and extends the recent ones announced by yu and yang j yu h yang existence of solutions for generalized variational inequality problems nonlinear anal 71 2009 e2327 e2330 and many others

conjugate duality in vector optimization and some applications to the vector variational inequality the aim of this paper is to extend the so called perturbation approach in order to deal with conjugate duality for constrained vector optimization problems to this end we use two conjugacy notions introduced in the past in the literature in the framework of set valued optimization as a particular case we consider a vector variational inequality which we rewrite in the form of a vector optimization problem the conjugate vector duals introduced in the first part allow us to introduce new gap functions for the vector variational inequality the properties in the definition of the gap functions are verified by using the weak and strong duality theorems