recognizable picture languages and domino tiling abstract in 2 giammarresi and restivo define the notion of local picture languages by giving a set of authorized 2 2 tiles over where is a boundary symbol which surrounds the pictures then they define the class of recognizable picture languages as the set of languages which can be obtained by projection of a local one this class is of interest since it admits several quite different characterizations 3 here we define the hv local picture languages where 2 2 tiles are replaced by horizontal and vertical dominoes so the horizontal and the vertical scanning can be done separately however we prove that every recognizable picture language can be obtained as a projection of a hv local language

a characterization of recognizable picture languages by tilings by finite sets as extension of the kleene star to pictures we introduce the operation of tiling we give a characterization of recognizable picture languages by intersection of tilings by finite sets of pictures

generalized equations and the generalized newton method we give some convergence results on the generalized newton method referred to by some authors as newton s method and the chord method when applied to generalized equations the main results of the paper extend the classical kantorovich results on newton s method to nonsmooth generalized equations our results also extend earlier results on nonsmooth equations due to eaves robinson josephy pang and chan

projection methods isotone projection cones and the complementarity problem one studies some iterative methods for solving complementarity problems explicit or implicit in hilbert spaces the iterative methods presented are based on the fixed point theory on the coincidence equations on convex cones and on some properties of projection operators onto a special cone named the isotone projection cone the ordering defined by the cone is essential for the complementarity theory the idea is to use systematically the ordering in the iterative methods for solving complementarity problems in this sense one shows that the isotone projection cone is a good instrument

a gauss seidel type method for dynamic nonlinear complementarity problems the dynamic nonlinear complementarity problem dncp consisting of a nonlinear differential system and a complementarity system has been used to formulate and study many dynamic problems in a gaus

geometric views of the generalized fischer burmeister function and its induced merit function abstract in this paper we study geometric properties of surfaces of the generalized fischer burmeister function and its induced merit function then a visualization is proposed to explain how the convergent behaviors are influenced by two descent directions in merit function approach based on the geometric properties and visualization we have more intuitive ideas about how the convergent behavior is affected by changing parameter furthermore geometric view indicates how to improve the algorithm to achieve our goal by setting proper value of the parameter in merit function approach

an r linearly convergent derivative free algorithm for nonlinear complementarity problems based on the generalized fischer burmeister merit function in the paper j s chen s pan a family of ncp functions and a descent method for the nonlinear complementarity problem computational optimization and applications 40 2008 389 404 the authors proposed a derivative free descent algorithm for nonlinear complementarity problems ncps by the generalized fischer burmeister merit function j p a b 12 a b p a b 2 and observed that the choice of the parameter p has a great influence on the numerical performance of the algorithm in this paper we analyze the phenomenon theoretically for a derivative free descent algorithm which is based on a penalized form of j p and uses a different direction from that of chen and pan more specifically we show that the algorithm proposed is globally convergent and has a locally r linear convergence rate and furthermore its convergence rate will become worse when the parameter p decreases numerical results are also reported for the test problems from mcplib which further verify the theoretical results obtained

a new method for a class of linear variational inequalities in this paper we introduce a new iterative scheme for the numerical solution of a class of linear variational inequalities each iteration of the method consists essentially only of a projection to a closed convex set and two matrix vector multiplications both the method and the convergence proof are very simple

characterizations of recognizable picture series the theory of two dimensional languages as a generalization of formal string languages was motivated by problems arising from image processing and pattern recognition and also concerns models of parallel computing here we investigate power series on pictures these are functions that map pictures to elements of a semiring and provide an extension of two dimensional languages to a quantitative setting we assign weights to different devices ranging from picture automata to tiling systems we will prove that for commutative semirings the behaviours of weighted picture automata are precisely alphabetic projections of series defined in terms of rational operations and also coincide with the families of series characterized by weighted tiling or weighted domino systems

a new class of iterative algorithms for approximation solvability of nonlinear variational inequalities abstract consider the convergence of the projection methods based on a new iterative algorithm for the approximation solvability of the following class of nonlinear variational inequality nvi problems find an element x k such that t x x x 0 for all x k where t k h is a mapping from a nonempty closed convex subset k of a real hilbert space h into h the new iterative procedure is characterized as a nonlinear variational inequality for any arbitrarily chosen initial point x0 k and for constants and 0 pt y k x k 1 y k x x k 1 0 for all x k and for k 0 where t x k y k x k x y k 0 for all x k this nonlinear variational inequality type algorithm has an equivalent projection formula x k 1 p k y k pt y k where y k p k x k t x k for the projection pk onto k

numerical stability and efficiency of penalty algorithms penalty algorithms have been somewhat forgotten due to numerical instabilities once believed to be inherent to those methods one usually has to solve a sequence of such problems and when the penalty factor decreases too fast the subproblems may become intractable moreover as the penalty factor decreases the unconstrained subproblem becomes ill conditioned and thus difficult to solve also in several intermediate computations numerical instability may show up the author proposes remedies to such problems and presents a wide class of numerically stable penalty algorithms the work is done in the more general context of variational inequality problems which encompasses optimization problems the author s results yield a family of globally convergent two step superlinearly convergent numerically stable algorithms for variational inequality problems finally issues in the numerically stable implementation of intermediate computations within those algorithms are discussed

projection methods algorithms and a new system of nonlinear variational inequalities abstract the convergence of projection methods is based on a new iterative algorithm for the approximation solvability of the following system of nonlinear variational inequalities snvi determine elements x y k such that t y x y x x 0 for all x k and for 0 and t x y x x y 0 for all x k and for 0 where t k h is a mapping from a nonempty closed convex subset k of a real hilbert space h into h this new class of generalized nonlinear variational inequalities reduces to standard class of nonlinear variational inequalities which are widely studied and applied to various problems arising from mathematical sciences optimization and control theory and other related fields

iterative methods for a class of complementarity problems abstract in this paper we propose and study an algorithm for a new class of complementarity problems of finding u r n such that u 0 tu a u 0 u tu a u 0 where t is a continuous mapping and a is a nonlinear transformation from r n into itself it is proved that the approximate solution obtained from the iterative scheme converges to the exact solution several special cases are also discussed

convergence rates in forward backward splitting forward backward splitting methods provide a range of approaches to solving large scale optimization problems and variational inequalities in which structures conducive to decomposition can be utilized apart from special cases where the forward step is absent and a version of the proximal point algorithm comes out efforts at evaluating the convergence potential of such methods have so far relied on lipschitz properties and strong monotonicity or inverse strong monotonicity of the mapping involved in the forward step the perspective mainly being that of projection algorithms here convergence is analyzed by a technique that allows properties of the mapping in the backward step to be brought in as well for the first time in such a general setting global and local contraction rates are derived moreover they are derived in a form which makes it possible to determine the optimal step size relative to certain constants associated with the given problem insights are thereby gained into the effects of shifting strong monotonicity between the forward and backward mappings when a splitting is selected

solving linear variational inequality problems by a self adaptive projection method we propose a self adaptive projection method for solving linear variational inequality problems and show its global convergence under mild conditions some numerical results are also addressed which indicate that the method is quite robust and efficient

the modulus based matrix double splitting iteration method for linear complementarity problems abstract for large sparse linear complementarity problems through reformulating them as implicit fixed point equations we propose a modulus based matrix double splitting mb ds iteration method by splitting the system matrices twice besides the convergence of this method is proved when the system matrix is a p matrix and an h matrix in some special cases we present the convergence regions and the optimal values for the parameter in order to show the efficiency of the mb ds iteration method and the effectiveness of the optimal parameter some corresponding numerical experiments are performed

on the existence and construction of t transitive closures in this paper it is shown that any fuzzy relation r on an arbitrary universe x has a t transitive closure the triangular norm t involved is not subject to any conditions this existential result can be turned into an explicit expression in the case of a left continuous triangular norm t furthermore this continuity restriction vanishes in the case of a finite universe x in that case the explicit expression can also be operationalized

an l error estimate for finite element solution of nonlinear elliptic problem with a source term the l error estimate for the finite element solution of nonlinear elliptic problem with a source term is discussed the lumped mass discretization method is used in the discretization and the error estimate o h 2 logh in l norm is obtained

a variable dimension solution approach for the general spatial price equilibrium problem algorithms are presented that are specifically designed for solving general nonlinear multicommodity spatial price equilibrium problems i e problems with nonlinear transportation cost functions nonlinear supply and demand functions inter commodity congestion effects intercommodity substitution and complementarity effects and interactions among transportation links and among spatially separated markets the algorithms are specializations of an iterative method for solving nonlinear complementarity problems that requires solving a system of nonlinear equations at each iteration the algorithms exploit the network structure of the problems to reduce the size of the system of equations to be solved at each iteration the decision rules for determining which equations are to be included in the system at each iteration are extremely simple and the remainder of the computational work is carried out by the nonlinear equation solver because of this the algorithms are very easy to implement with readily available software in addition since the decision rules only require sign information only the final system needs to be solved with precision

asymmetric variational inequality problems over product sets applications and iterative methods in this paper we i describe how several equilibrium problems can be uniformly modelled by a finite dimensional asymmetric variational inequality defined over a cartesian product of sets and ii investigate the local and global convergence of various iterative methods for solving such a variational inequality problem because of the special cartesian product structure these iterative methods decompose the original variational inequality problem into a sequence of simpler variational inequality subproblems in lower dimensions the resulting decomposition schemes often have a natural interpretation as some adjustment processes

asymptotic analysis for penalty and barrier methods in variational inequalities we study the convergence of a class of penalty and barrier methods for solving monotone variational inequalities with constraints this class of methods is an extension of penalty and barrier methods for convex optimization to the setting of variational inequalities primal convergence is established under weaker conditions than usual the solution set is supposed either to be a compact set or for the case of interior barrier methods the sum of a compact set and a linear space dual convergence is also analyzed the analysis strongly exploits a new formula related to recession calculus

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

a new algorithm for solving variational inequalities with application to the traffic assignment problem the variational inequality problem in euclidian space is formulated as a nonconvex nondifferentiable optimization problem we show that any stationary point is optimal and we propose a solution algorithm that decreases the nondifferential objective monotonically application to the asymmetric traffic assignment problem is considered

minimization algorithm of fuzzy finite automata in this paper a class of fuzzy finite automata corresponding to the mealy type of ordinary automata is formulated and also two types of statewise equivalence relations are introduced from the equivalence relations a minimal form is defined and a minimization algorithm of the mealy type of fuzzy finite automata is obtained

a general descent framework for the monotone variational inequality problem we present a framework for descent algorithms that solve the monotone variational inequality problem vip v which consists in finding a solutionv v satisfyings v t v v 0 for allv v this unified framework includes as special cases some well known iterative methods and equivalent optimization formulations a descent method is developed for an equivalent general optimization formulation and a proof of its convergence is given based on this unified logarithmic framework we show that a variant of the descent method where each subproblem is only solved approximately is globally convergent under certain conditions

a globally convergent newton method for solving strongly monotone variational inequalities variational inequality problems have been used to formulate and study equilibrium problems which arise in many fields including economics operations research and regional sciences for solving variational inequality problems various iterative methods such as projection methods and the nonlinear jacobi method have been developed these methods are convergent to a solution under certain conditions but their rates of convergence are typically linear in this paper we propose to modify the newton method for variational inequality problems by using a certain differentiable merit function to determine a suitable step length the purpose of introducing this merit function is to provide some measure of the discrepancy between the solution and the current iterate it is then shown that under the strong monotonicity assumption the method is globally convergent and under some additional assumptions the rate of convergence is quadratic limited computational experience indicates the high efficiency of the proposed method

accelerating the convergence of the diagonalization and projection algorithms for finite dimensional variational inequalities this paper presents an acceleration step for the linearly convergent diagonalization and projection algorithms for finite dimensional variational inequalities which is reminiscent of a partan step in nonlinear programming after establishing the convergence of this technique for both algorithms several numerical examples are presented to illustrate the sometimes dramatic savings in computation time which this simple acceleration step yields

generalized nash games and quasi variational inequalities abstract a generalized nash game is an n person noncooperative game with nondisjoint strategy sets other names for this game form include social equilibria and pseudo nash games this paper explores both the qualitative and quantitative properties of such games through the use of quasi variational inequality theory several interesting relationships between the variational and quasi variational inequality forms of this class of games are described and the practical implementation of generalized nash games are explored at length

computing nonlinear network equilibria this paper examines the problem of computing nonlinear network equilibria using a newton iteration by exploiting the network structure we are able to show that the iteration is globally convergent monotonic and locally quadratically convergent using only simple algebraic arguments

projected successive overrelaxation method for finite element solutions to the dirichlet problem for a system of nonlinear elliptic equations abstract in this paper we consider the projected successive overrelaxation sor method for obtaining finite element solutions applied to the dirichlet problem for a system of nonlinear elliptic equations these equations arise in gas dynamics and chemical reactions the jacobian matrix for the nonlinear equations is not symmetric so that there is no longer an associated minimization problem a convergence proof of the projected sor method is established by using a contraction argument because minimization techniques are not applicable we also discuss the optimum relaxation parameter based upon the linear sor theory finally we show some numerical examples to indicate the effectiveness of the projected sor method

generalized descent methods for asymmetric systems of equations we consider generalizations of the steepest descent algorithm for solving asymmetric systems of equations we first show that if the system is linear and is defined by the matrix m then the method converges if m2 is positive definite we also establish easy to verify conditions on the matrix m that ensure that m2 is positive definite and develop a scaling procedure that extends the class of matrices that satisfy the convergence conditions in addition we establish a local convergence result for nonlinear systems defined by uniformly monotone maps and discuss a class of general descent methods all of the methods that we consider reduce to standard nonlinear programming algorithms for equivalent optimization problems when the jacobian of the underlying problem map is symmetric we interpret the convergence conditions for the generalized steepest descent algorithms as restricting the degree of asymmetry of the problem map

schutzenberger s theorem on formal power series follows from kleene s theorem we derive schutzenberger s characterisation of the set of recognizable formal power series as a formal corollary from kleene s characterisation of the set of regular languages

sensitivity analysis for the asymmetric network equilibrium problem we consider the asymmetric continuous traffic equilibrium network model with fixed demands where the travel cost on each link of the transportation network may depend on the flow on this as well as other links of the network and we perform stability and sensitivity analysis assuming that the travel cost functions are monotone we first show that the traffic equlibrium pattern depends continuously upon the assigned travel demands and travel cost functions we then focus on the delicate question of predicting the direction of the change in the traffic pattern and the incurred travel costs resulting from changes in the travel cost functions and travel demands and attempt to elucidate certain counter intuitive phenomena such as braess paradox our analysis depends crucially on the fact that the governing equilibrium conditions can be formulated as a variational inequality

averaging schemes for variational inequalities and systems of equations we study averaging methods for solving variational inequalities whose underlying maps are nonexpansive and for solving systems of asymmetric equations our goal is to establish global convergence results using weaker assumptions than are traditional in the literature we examine averaging schemes for relaxation algorithms and for their specialization as projection and linearization methods and as cohen s auxiliary framework for solving systems of equations we consider averaging for a general class of methods that includes as a special case a generalized steepest descent method we also develop a new interpretation of a norm condition typically used for establishing convergence of relaxation schemes by associating it with a strong f monotonicity condition

finite l fuzzy machines abstract for finite l fuzzy machines we develop behaviour reduction and minimization theory here l stands for l 0 1 where l is a totally ordered set with universal bounds 0 and 1 and the operations are join and meet the most essential results include investigating behaviour equivalence reduction and minimization problems and their algorithmical decidability

adding pebbles to weighted automata easy specification efficient evaluation we extend weighted automata and weighted rational expressions with 2 way moves and reusable pebbles we show with examples from natural language modeling and quantitative model checking that weighted expressions and automata with pebbles are more expressive and allow much more natural and intuitive specifications than classical ones we extend kleene schutzenberger theorem showing that weighted expressions and automata with pebbles have the same expressive power we focus on an efficient translation from expressions to automata we also prove that the evaluation problem for weighted automata can be done very efficiently if the number of reusable pebbles is low

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

monadic second order logic over rectangular pictures and recognizability by tiling systems abstract it is shown that a set of pictures rectangular arrays of symbols is recognized by a finite tiling system iff it is definable in existential monadic second order logic as a consequence finite tiling systems constitute a notion of recognizability over two dimensional inputs which at the same time generalizes finite state recognizability over strings and also matches a natural logic the proof is based on the ehrenfeucht fraisse technique for first order logic and an implementation of threshold counting within tiling systems

collage of two dimensional words we consider a new operation on one dimensional resp two dimensional word languages obtained by piling up one on top of the other words of a given recognizable language resp two dimensional recognizable language on a previously empty one dimensional resp two dimensional array the resulting language is the set of words seen from above a position in the array is labeled by the topmost letter we show that in the one dimensional case the language is always recognizable this is no longer true in the two dimensional case which is shown by a counter example and we investigate in which particular cases the result may still hold

a column generation technique for the computation of stationary points in two recent papers eaves showed that lemke s algorithm can be used to compute a stationary point of an affine function over a polyhedral set this paper proposes an alternative method which is based on parametric principal pivoting the proposed method involves solving systems of linear equations and parametric linear subprograms over the given polyhedral set an obvious advantage of the method is that any special structure of the polyhedral set can be exploited profitably in the solution of the subprograms

rapid and brief communications kernel direct discriminant analysis and its theoretical foundation in this paper the method of kernel direct discriminant analysis is analyzed from a new viewpoint and its theoretical foundation is revealed based on this result an efficient and robust method is proposed that is the qr decomposition on the small size matrix is adopted and then a small eigenvalue problem is solved finally experimental results on orl face database show that the proposed method is effective and feasible

construction of fuzzy automata from fuzzy regular expressions li and pedrycz have proved fundamental results that provide different equivalent ways to represent fuzzy languages with membership values in a lattice ordered monoid and generalize the well known results of the classical theory of formal languages in particular they have shown that a fuzzy language over an integral lattice ordered monoid can be represented by a fuzzy regular expression if and only if it can be recognized by a fuzzy finite automaton however they did not give any efficient method for constructing an equivalent fuzzy finite automaton from a given fuzzy regular expression in this paper we provide such an efficient method transforming scalars appearing in a fuzzy regular expression ainto letters of the new extended alphabet we convert the fuzzy regular expression ato an ordinary regular expression a r then starting from an arbitrary nondeterministic finite automaton a that recognizes the language a r represented by the regular expression a r we construct fuzzy finite automata a a and a a r with the same or even less number of states than the automaton a which recognize the fuzzy language a represented by the fuzzy regular expression a the starting nondeterministic finite automaton a can be obtained from a r using any of the well known constructions for converting regular expressions to nondeterministic finite automata such as glushkov mcnaughton yamada s position automaton brzozowski s derivative automaton antimirov s partial derivative automaton or ilie yu s follow automaton

solving a class of linear projection equations many interesting and important constrained optimization problems in mathematical programming can be translated into an equivalent linear projection equation u p omega u mu q here p omega cdot is the orthogonal projection on some convex set omega e g omega bbb r n and m is a positive semidefinite matrix this paper presents some new methods for solving a class of linear projection equations the search directions of these methods are straighforward extensions of the directions in traditional methods for unconstrained optimization based on the idea of a projection and contraction method 7 we get a simple step length rule and are able to obtain global linear convergence

further applications of a splitting algorithm to decomposition in variational inequalities and convex programming a classical method for solving the variational inequality problem is the projection algorithm we show that existing convergence results for this algorithm follow from one given by gabay for a splitting algorithm for finding a zero of the sum of two maximal monotone operators moreover we extend the projection algorithm to solveany monotone affine variational inequality problem when applied to linear complementarity problems we obtain a matrix splitting algorithm that is simple and for linear quadratic programs massively parallelizable unlike existing matrix splitting algorithms this algorithm converges under no additional assumption on the problem when applied to generalized linear quadratic programs we obtain a decomposition method that unlike existing decomposition methods can simultaneously dualize the linear constraints and diagonalize the cost function this method gives rise to highly parallelizable algorithms for solving a problem of deterministic control in discrete time and for computing the orthogonal projection onto the intersection of convex sets

an iterative scheme for variational inequalities in this paper we introduce and study a general iterative scheme for the numerical solution of finite dimensional variational inequalities this iterative scheme not only contains as special cases the projection linear approximation and relaxation methods but also induces new algorithms then we show that under appropriate assumptions the proposed iterative scheme converges by establishing contraction estimates involving a sequence of norms in en induced by symmetric positive definite matrices gm thus in contrast to the above mentioned methods this technique allows the possibility of adjusting the norm at each step of the algorithm this flexibility will generally yield convergence under weaker assumptions

a projection filter method for solving nonlinear complementarity problems the josephy newton method attacks nonlinear complementarity problems which consists of solving possibly inexactly a sequence of linear complementarity problems under appropriate regularity assumptions this method is known to be locally superlinearly convergent utilizing the filter method we presented a new globalization strategy for this newton method applied to nonlinear complementarity problem without any merit function the strategy is based on the projection proximal point and filter methodology our linesearch procedure uses the regularized newton direction to force global convergence by means of a projection step which reduces the distance to the solution of the problem the resulting algorithm is globally convergent to a solution under natural assumptions locally superlinear rate of convergence was established

a class of parallel nonlinear multisplitting relaxation methods for the large sparse nonlinear complementarity problems abstract by making use of the nonlinear multisplitting and the nonlinear relaxation techniques we present in this paper a class of parallel nonlinear multisplitting successive overrelaxation methods for solving the large sparse nonlinear complementarity problems on the modern high speed multiprocessors these new methods particularly include the so called nonlinear multisplitting sor newton method under suitable conditions we establish the local convergence theories of the new methods and investigate their asymptotic convergence rates a lot of numerical results show that our new methods are feasible and efficient for parallel solving the nonlinear complementarity problems

a system of nonsmooth equations solver based upon subgradient method in this paper a subgradient method is developed to solve the system of nonsmooth equations first the system of nonsmooth equations is transformed into a nonsmooth optimization problem with zero minimal objective function value then a subgradient method is applied to solve the nonsmooth optimization problem during the processes the pre known optimal objective function value is adopted to update step sizes the corresponding convergence results are established as well several numerical experiments and applications show that the proposed method is efficient and robust

face recognition using kernel direct discriminant analysis algorithms techniques that can introduce low dimensional feature representation with enhanced discriminatory power is of paramount importance in face recognition fr systems it is well known that the distribution of face images under a perceivable variation in viewpoint illumination or facial expression is highly nonlinear and complex it is therefore not surprising that linear techniques such as those based on principle component analysis pca or linear discriminant analysis lda cannot provide reliable and robust solutions to those fr problems with complex face variations in this paper we propose a kernel machine based discriminant analysis method which deals with the nonlinearity of the face patterns distribution the proposed method also effectively solves the so called small sample size sss problem which exists in most fr tasks the new algorithm has been tested in terms of classification error rate performance on the multiview umist face database results indicate that the proposed methodology is able to achieve excellent performance with only a very small set of features being used and its error rate is approximately 34 and 48 of those of two other commonly used kernel fr approaches the kernel pca kpca and the generalized discriminant analysis gda respectively

an equivalence between two algorithms for quadratic programming in this paper we demonstrate that the van de panne whinston symmetric simplex method when applied to a certain implicit formulation of a quadratic program generates the same sequence of primal feasible vectors as does the von hohenbalken simplicial decomposition algorithm specialized to the same program such an equivalence of the two algorithms extends earlier results for a least distance program due to cottle djang

uncapacitated point to multipoint network flow problem and its application to multicasting in telecommunication networks abstract this paper introduces an uncapacitated point to multipoint network flow problem where a convex arc cost and demand splitting is introduced this problem arises from multicast routing in telecommunication networks such as the internet protocol network multiple tree routes are used to use the network resources efficiently the proposed method adds extra tree routes until it satisfies the target conditions this method splits the multicast traffic demand into the chosen tree routes in this study a mathematical model was developed and the conditions for traffic splitting were optimized the convergence of the algorithm was obtained under monotonically increasing and strictly convex conditions on the arc cost function a modified algorithm was proposed for a practical multicasting method various experiments were carried and the results show that the new multicasting method is fairly effective in improving the quality of service with only two or three multiple tree routes

fuzzy language on free monoid in this paper we shall introduce the notion of fuzzy regular language adjunctive language and dense language and discuss their algebraic character and algebraic properties

rapid and brief communication laplacian linear discriminant analysis a novel linear discriminant criterion function is proved to be equal to fisher s criterion function the analysis of the function is linked to spectral decomposition of the laplacian of a graph moreover the function is maximized using two algorithms experimental results show the effectiveness and some specific characteristics of our algorithms

a new projection method for variational inequality problems we propose a new projection algorithm for solving the variational inequality problem where the underlying function is continuous and satisfies a certain generalized monotonicity assumption e g it can be pseudomonotone the method is simple and admits a nice geometric interpretation it consists of two steps first we construct an appropriate hyperplane which strictly separates the current iterate from the solutions of the problem this procedure requires a single projection onto the feasible set and employs an armijo type linesearch along a feasible direction then the next iterate is obtained as the projection of the current iterate onto the intersection of the feasible set with the halfspace containing the solution set thus in contrast with most other projection type methods only two projection operations per iteration are needed the method is shown to be globally convergent to a solution of the variational inequality problem under minimal assumptions preliminary computational experience is also reported

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

schwarz algorithm for the solution of variational inequalities with nonlinear source terms numerical solution of variational inequalities of obstacle type associated with some free boundary problems with nonlinear source terms is considered iterative methods based on the combination of the domain decomposition technique and the newton like approach are proposed for solving discrete obstacle problems arising from the continuous piecewise linear finite element approximation of the problems the calculation processes are easily to be parallelized the convergence and specially the convergent rate of the algorithms are obtained

asymptotic convergence analysis of the forward backward splitting algorithm the asymptotic convergence of the forward backward splitting algorithm for solving equations of type 0 t z is analyzed where t is a multivalued maximal monotone operator in the n dimensional euclidean space when the problem has a nonempty solution set and t is split in the form t h with being maximal monotone and h being co coercive with modulus greater than convergence rates are shown under mild conditions to be linear superlinear or sublinear depending on how rapidly 1 and h 1 grow in the neighborhoods of certain specific points as a special case when both and h are polyhedral functions we get r linear convergence and 2 step q linear convergence without any further assumptions on the strict monotonicity on t or on the uniqueness of the solution as another special case when h 0 the splitting algorithm reduces to the proximal point algorithm and we get new results which complement r t rockafellar s and f j luque s earlier results on the proximal point algorithm

a variational inequality approach for the determination of oligopolistic market equilibrium this paper presents an alternative approach to that by murphy sherali and soyster 13 for computing market equilibria with mathematical programming methods this approach is based upon a variational inequality representation of the problem and the use of a diagonalization relaxation algorithm

equivalence of some quadratic programming algorithms we formulate a general algorithm for the solution of a convex but not strictly convex quadratic programming problem conditions are given under which the iterates of the algorithm are uniquely determined the quadratic programming algorithms of fletcher gill and murray best and ritter and van de panne and whinston dantzig are shown to be special cases and consequently are equivalent in the sense that they construct identical sequences of points the various methods are shown to differ only in the manner in which they solve the linear equations expressing the kuhn tucker system for the associated equality constrained subproblems equivalence results have been established by goldfarb and djang for the positive definite hessian case our analysis extends these results to the positive semi definite case

role of twice frechet differentiable mappings in general auxiliary problem principle abstract the approximation solvability of the following class of nonlinear variational inequality problems nvip based on the general auxiliary problem principle lapp is discussed find an element k such that x x x f x f x o for all x k where t k e is a nonlinear mapping from a nonempty closed convex subset k of a reflexive banach space e into its dual e and f k r is a continuous convex functional on k

fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids we study fuzzy finite automata in which all fuzzy sets are defined by membership functions whose codomain forms a lattice ordered monoid l for these l fuzzy finite automata l ffa for short we provide necessary and sufficient conditions for the extendability of the state transition function it is shown that nondeterministic l ffa nl ffa for short are more powerful than deterministic l ffa dl ffa for short then we give necessary and sufficient conditions for the simulation of an nl ffa by an equivalent dl ffa next we turn to the closure properties of languages defined by l ffas we establish closure under the regular operations and provide conditions for closure under intersection and reversal in particular we show that the family of fuzzy languages accepted by dl ffas is not closed under kleene closure operation and the family of fuzzy languages accepted by nl ffas is not closed under complement operation furthermore we introduce the notions of l fuzzy regular expressions and give the kleene theorem for nl ffas the description of dl ffas by l fuzzy regular expressions is also given finally we investigate the level structures of l ffas our results provide some insight as to what extend properties of l ffas and their languages depend on the algebraic properties of l

generalized discriminant analysis using a kernel approach we present a new method that we call generalized discriminant analysis gda to deal with nonlinear discriminant analysis using kernel function operator the underlying theory is close to the support vector machines svm insofar as the gda method provides a mapping of the input vectors into high dimensional feature space in the transformed space linear properties make it easy to extend and generalize the classical linear discriminant analysis lda to nonlinear discriminant analysis the formulation is expressed as an eigenvalue problem resolution using a different kernel one can cover a wide class of nonlinearities for both simulated data and alternate kernels we give classification results as well as the shape of the decision function the results are confirmed using real data to perform seed classification

parallel newton methods for the nonlinear complementary problem in this paper we discuss how the basic newton method for solving the nonlinear complementarity problem can be implemented in a parallel computation environment we propose some synchronized and asynchronous newton methods and establish their convergence

a quasisecant method for solving a system of nonsmooth equations in this paper the solution of nonsmooth equations is studied we first transform the problem into an equivalent nonsmooth optimization problem and then the quasisecant method is introduced to solve it some nonsmooth equations that have arisen from bilevel programming problems are solved by our proposed method the numerical results show the effectiveness and efficiency of our proposed method

weighted finite automata over strong bimonoids we investigate weighted finite automata over strings and strong bimonoids such algebraic structures satisfy the same laws as semirings except that no distributivity laws need to hold we define two different behaviors and prove precise characterizations for them if the underlying strong bimonoid satisfies local finiteness conditions moreover we show that in this case the given weighted automata can be determinized

real and complex monotone communication games noncooperative game theoretic tools have been increasingly used to study many important resource allocation problems in communications networking smart grids and portfolio optimization in this paper we consider a general class of convex nash equilibrium problems neps where each player aims at solving an arbitrary smooth convex optimization problem differently from most of current works we do not assume any specific structure for the players problems and we allow the optimization variables of the players to be matrices in the complex domain our main contribution is the design of a novel class of distributed asynchronous best response algorithms suitable for solving the proposed neps even in the presence of multiple solutions the new methods whose convergence analysis is based on variational inequality vi techniques can select among all the equilibria of a game those that optimize a given performance criterion at the cost of limited signaling among the players this is a major departure from existing best response algorithms whose convergence conditions imply the uniqueness of the ne some of our results hinge on the use of vi problems directly in the complex domain the study of these new kind of vis also represents a noteworthy innovative contribution we then apply the developed methods to solve some new generalizations of single input single output siso and multiple input multiple output mimo games in cognitive radio systems showing a considerable performance improvement over classical pure noncooperative schemes

a unified description of iterative algorithms for traffic equilibria the purpose of this paper is to provide a unified description of iterative algorithms for the solution of traffic equilibrium problems we demonstrate that a large number of well known solution techniques can be described in a unified manner through the concept of partial linearization and establish close relationships with other algorithmic classes for nonlinear programming and variational inequalities in the case of nonseparable travel costs the class of partial linearization algorithms are shown to yield new results in the theory of finite dimensional variational inequalities the possibility of applying truncated algorithms within the framework is also discussed

solving variational inequality and fixed point problems by line searches and potential optimization we introduce a general adaptive line search framework for solving fixed point and variational inequality problems our goals are to develop iterative schemes that i compute solutions when the underlying map satisfies properties weaker than contractiveness for example weaker forms of nonexpansiveness ii are more efficient than the classical methods even when the underlying map is contractive and iii unify and extend several convergence results from the fixed point and variational inequality literatures to achieve these goals we introduce and study joint compatibility conditions imposed upon the underlying map and the iterative step sizes at each iteration and consider line searches that optimize certain potential functions as a special case we introduce a modified steepest descent method for solving systems of equations that does not require a previous condition from the literature the square of the jacobian matrix is positive definite since the line searches we propose might be difficult to perform exactly we also consider inexact line searches

a relaxed projection method for variational inequalities this paper presents a modification of the projection methods for solving variational inequality problems each iteration of the proposed algorithm consists of projection onto a halfspace containing the given closed convex set rather than the latter set itself the algorithm can thus be implemented very easily and its global convergence to the solution can be established under suitable conditions

complexity of two dimensional patterns in dynamical systems such as cellular automata and iterated maps it is often useful to look at a language or set of symbol sequences produced by the system there are well established classification schemes such as the chomsky hierarchy with which we can measure the complexity of these sets of sequences and thus the complexity of the systems which produce them in this paper we look at the first few levels of a hierarchy of complexity for two or more dimensional patterns we show that several definitions of regular language or local rule that are equivalent in d 1 lead to distinct classes in d 2 we explore the closure properties and computational complexity of these classes including undecidability and l nl and np completeness results we apply these classes to cellular automata in particular to their sets of fixed and periodic points finite time images and limit sets we show that it is undecidable whether a ca in d 2 has a periodic point of a given period and that certain local lattice languages are not finite time images or limit sets of any ca we also show that the entropy of a d dimensional ca s finite time image cannot decrease faster than t d unless it maps every initial condition to a single homogeneous state

tile rewriting grammars and picture languages tile rewriting grammars trg are a new model for defining picture languages a rewriting rule changes a homogeneous rectangular subpicture into an isometric one tiled with specified tiles derivation and language generation with trg rules are similar to context free grammars a normal form and some closure properties are presented we prove this model has greater generative capacity than the tiling systems of giammarresi and restivo and the grammars of matz another generalization of context free string grammars to 2d examples are shown for pictures made by nested frames and spirals

a truly globally convergent newton type method for the monotone nonlinear complementarity problem the josephy newton method for solving a nonlinear complementarity problem consists of solving possibly inexactly a sequence of linear complementarity problems under appropriate regularity assumptions this method is known to be locally superlinearly convergent to enlarge the domain of convergence of the newton method some globalization strategy based on a chosen merit function is typically used however to ensure global convergence to a solution some additional restrictive assumptions are needed these assumptions imply boundedness of level sets of the merit function and often even global uniqueness of the solution we present a new globalization strategy for monotone problems which is not based on any merit function our linesearch procedure utilizes the regularized newton direction and the monotonicity structure of the problem to force global convergence by means of a computationally explicit projection step which reduces the distance to the solution set of the problem the resulting algorithm is truly globally convergent in the sense that the subproblems are always solvable and the whole sequence of iterates converges to a solution of the problem without any regularity assumptions in fact the solution set can even be unbounded each iteration of the new method has the same order of computational cost as an iteration of the damped newton method under natural assumptions the local superlinear rate of convergence is also achieved

computation of the greatest simulations and bisimulations between fuzzy automata recently two types of simulations forward and backward simulations and four types of bisimulations forward backward forward backward and backward forward bisimulations between fuzzy automata have been introduced if there is at least one simulation bisimulation of some of these types between the given fuzzy automata it has been proved that there is the greatest simulation bisimulation of this kind in the present paper for any of the above mentioned types of simulations bisimulations we provide an efficient algorithm for deciding whether there is a simulation bisimulation of this type between the given fuzzy automata and for computing the greatest one whenever it exists the algorithms are based on the method developed in ignjatovic et al on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations fuzzy sets syst 161 2010 3081 3113 which comes down to the computing of the greatest post fixed point contained in a given fuzzy relation of an isotone function on the lattice of fuzzy relations

sparse multinomial kernel discriminant analysis smkda dimensionality reduction via canonical variate analysis cva is important for pattern recognition and has been extended variously to permit more flexibility e g by kernelizing the formulation this can lead to over fitting usually ameliorated by regularization here a method for sparse multinomial kernel discriminant analysis smkda is proposed using a sparse basis to control complexity it is based on the connection between cva and least squares and uses forward selection via orthogonal least squares to approximate a basis generalizing a similar approach for binomial problems classification can be performed directly via minimum mahalanobis distance in the canonical variates smkda achieves state of the art performance in terms of accuracy and sparseness on 11 benchmark datasets

a hybrid method for the solution of some multi commodity spatial equilibrium problems this paper describes a hybrid method for solving the multi commodity transportation and transshipment spatial equilibrium models the method is basically a specialization of the block successive overrelaxation method for solving a linear complementarity problem with certain block structure and consists of solving a sequence of subproblems of the single commodity type these subproblems are solved by a special purpose principal pivoting algorithm developed in an earlier paper under some mild conditions convergence of the proposed method is established finally computational experience of solving some fairly large randomly generated problems by the proposed hybrid method is presented

on the solution of variational inequalities by the ellipsoid method variational inequalities provide a convenient mathematical approach for unifying results relating to extremum and equilibrium problems in this paper we demonstrate the applicability of the ellipsoid method to solve monotone variational inequalities a convergence proof is given which for example in case of convex optimization explains the linear convergence of the record points we compare this result with goffin s convergence proof by extending his proof technique to the constrained case in the appendix