convergence of the two step combined method and uniqueness of the solution of nonlinear operator equations local convergence of the two step differential difference method for solving nonlinear operator equations for generalized lipschitz conditions for frechet derivatives of the first and second order and divided differences of the first order has been proven there have been found estimations of the convergence ball s radii of this method and the uniqueness ball of solution of nonlinear equations there has been established the superquadratical order of the convergence of the two step combined method and a comparison of the results with the known ones has been made

the primal dual active set strategy as a semismooth newton method this paper addresses complementarity problems motivated by constrained optimal control problems it is shown that the primal dual active set strategy which is known to be extremely efficient for this class of problems and a specific semismooth newton method lead to identical algorithms the notion of slant differentiability is recalled and it is argued that the max function is slantly differentiable in lp spaces when appropriately combined with a two norm concept this leads to new local convergence results of the primal dual active set strategy global unconditional convergence results are obtained by means of appropriate merit functions

a degree theoretic approach to parametric nonsmooth equations with multivalued perturbed solution sets this paper studies the sensitivity of a parametric nonsmooth equation using degree theory and set valued analysis under the assumption of existence of an approximating function of a certain kind we investigate the existence continuity and differentiability of the set valued solutions of the parametric equation our analysis is a synthesis of the work of several authors king and rockafellar 1992 gowda and pang 1991 robinson 1991 applications of the derived results to the convergence of newton s method and to the sensitivity analysis of parametric complementarity problems and variational inequalities will be discussed

a semismooth equation approach to the solution of nonlinear complementarity problems in this paper we present a new algorithm for the solution of nonlinear complementarity problems the algorithm is based on a semismooth equation reformulation of the complementarity problem we exploit the recent extension of newton s method to semismooth systems of equations and the fact that the natural merit function associated to the equation reformulation is continuously differentiable to develop an algorithm whose global and quadratic convergence properties can be established under very mild assumptions other interesting features of the new algorithm are an extreme simplicity along with a low computational burden per iteration we include numerical tests which show the viability of the approach

koszul complexes and symmetric forms over the punctured affine space let x be a regular separated scheme of finite krull dimension and let u n x subset a n x be the punctured affine n space over x we show that the total graded witt ring of u n x is a free graded module over the total graded witt ring of x with two generators 1 and epsilon the second generator satisfies the equation epsilon 2 1 when n 1 and epsilon 2 0 when n geq 2

a unifying local semilocal convergence analysis and applications for two point newton like methods in banach space abstract we provide a local as well as a semilocal convergence analysis for two point newton like methods in a banach space setting under very general lipschitz type conditions our equation contains a frechet differentiable operator f and another operator g whose differentiability is not assumed using more precise majorizing sequences than before we provide sufficient convergence conditions for newton like methods to a locally unique solution of equation f x g x 0 in the semilocal case we show under weaker conditions that our error estimates on the distances involved are finer and the information on the location of the solution at least as precise as in earlier results in the local case a larger radius of convergence is obtained several numerical examples are provided to show that our results compare favorably with earlier ones as a special case we show that the famous newton kantorovich hypothesis is weakened under the same hypotheses as the ones contained in the newton kantorovich theorem

string periods in the order preserving model abstract in the order preserving model two strings match if they share the same relative order between the characters at the corresponding positions this model is quite recent but it has already attracted significant attention because of its applications in data analysis we introduce several types of periods in this setting op periods then we give algorithms to compute these periods in time o n o n log log n o n log 2 log n log log log n o n log n depending on the type of periodicity in the most general variant the number of different op periods can be as big as n 2 and a compact representation is needed our algorithms require novel combinatorial insight into the properties of op periods in particular we characterize the fine wilf property for coprime op periods

newton s method and quasi newton sqp method for general lc1 constrained optimization in this paper we study the second order sufficient and necessary conditions for lc 1 constrained optimization problems present newton methods and quasi newton sqp methods for this kind of problems and establish locally linear and superlinear convergence this work extends the classical theory of convex smooth minimization to general lc 1 constrained optimization

fine and wilf s theorem for three periods and a generalization of sturmian words we extend the theorem of fine and wilf to words having three periods we then define the set 3 per of words of maximal length for which such result does not apply we prove that the set 3 per and the sequences of complexity 2n 1 introduced by arnoux and rauzy to generalize sturmian words have the same set of factors

semismooth karush kuhn tucker equations and convergence analysis of newton and quasi newton methods for solving these equations there are several forms of systems of nonsmooth equations which are equivalent to the karush kuhn tucker kkt system of a nonlinearly constrained optimization problem nlp if the nlp is twice continuously differentiable and the hessian functions of its objective and constraint functions are locally lipschitzian then these kkt equations are strongly semismooth if furthermore the linear independence condition and the strong second order sufficiency condition are satisfied at a kkt point then the generalized jacobians of these kkt equations are nonsingular at that point and the sequence generated by the generalized newton method converges to this point q quadratically however direct application of quasi newton methods cannot guarantee q superlinear convergence we present a mixed quasi newton method which converges q superlinearly with common symmetrical updating rules under the above conditions for the generalized newton method superlinear convergence of the primal variables and global convergence are also discussed

mathematical foundations of nonsmooth embedding methods this paper establishes a mathematical foundation for application of the well known classical embedding approach to a class of nonsmooth functions using a recently developed analogue of the derivative in cases where the functions involved fail to be differentiable in the usual sense as part of this development we show how to obtain an extension to this case of the classical hadamard theorem giving conditions for a map of n to itself to be a homeomorphism

episturmian words and episturmian morphisms infinite episturmian words are a generalization of sturmian words which includes the arnoux rauzy sequences we continue their study and that of episturmian morphisms begun previously in relation with the action of the shift operator palindromic and periodic factors of these words are described we consider in particular the case where these words are generated by morphisms and introduce then a notion of intercept generalizing that of sturmian words finally we prove that the frequencies of the factors in a strong sense do exist for all episturmian words

smoothing methods and semismooth methods for nondifferentiable operator equations we consider superlinearly convergent analogues of newton methods for nondifferentiable operator equations in function spaces the superlinear convergence analysis of semismooth methods for nondifferentiable equations described by a locally lipschitzian operator in rn is based on rademacher s theorem which does not hold in function spaces we introduce a concept of slant differentiability and use it to study superlinear convergence of smoothing methods and semismooth methods in a unified framework we show that a function is slantly differentiable at a point if and only if it is lipschitz continuous at that point an application to the dirichlet problems for a simple class of nonsmooth elliptic partial differential equations is discussed

standard sturmiam morphisms abstract we give a characterization of morphisms which preserve finite and infinite standard sturmian words the class of such morphisms coincides with the monoid d e of the endomorphisms of a where a a b generated by the two elementary morphisms e which interchanges the letter a with b and d which is the fibonacci morphism defined as d a ab d b a some new properties of these morphisms are shown in particular we prove the following result let x n n 0 be the sequence of sets inductively defined as x 0 e x 1 a x n 1 ax n for n 1 where e denotes the empty word and is the operator of left palindrome closure associating to each word w the shortest word having w as suffix for all n 0 one has x n 1 e g d x n a where denotes the identity map from this we derive a new characterization of the set per of all words w having two periods p and q which are coprimes and such that w p q 2 indeed one has that per aa xcup n 0 e l od x n a

a homotopy continuation method for solving normal equations in this paper we present a continuation method for solving normal equations generated byc 2 functions and polyhedral convex sets we embed the normal map into a homotopyh and study the existence and characteristics of curves inh 1 0 starting at a specificd point we prove the convergence of such curves to a solution of the normal equation under some conditions on the polyhedral convex setc and the functionf we prove that the curve will have finite are length if the normal map associated with the derivative df and the critical conek is coherently oriented at each zero of the normal mapf c inside a certain ball of n 1998 the mathematical programming society inc published by elsevier science b v

triangular witt groups part ii from usual to derived we establish that the derived witt group is isomorphic to the usual witt group when 2 is invertible this key result opens the ali baba s cave of triangular witt groups linking the abstract results of part i to classical questions for the usual witt group for commercial purposes we survey the future applications of triangular witt groups in the introduction we also establish a connection between odd indexed witt groups and formations finally we prove that over a commutative local ring in which 2 is a unit the shifted derived witt groups are all zero but the usual one

some quadrature based versions of the generalized newton method for solving nonsmooth equations abstract in this paper modifications of a generalized newton method based on some rules of quadrature are studied the methods considered are newton like iterative schemes for numerical solving systems of nonsmooth equations some mild conditions are given that ensure superlinear convergence to a solution moreover a parameterized version of the midpoint version is presented finally results of numerical tests are established

a periodicity lemma for partial words abstract we investigate the function l h p q called here the length function such that l h p q is the minimum length which guarantees that a natural extension of the periodicity lemma is valid for partial words with h holes and so called strong periods p q in a series of papers the formulae for the length function in terms of p and q were provided for each fixed h 7 we demystify the generic structure of such formulae and give a complete characterization of the length function for any parameter h expressed in terms of a piecewise linear function with o h pieces we also show how to evaluate the length function in o log p log q time which is an improvement upon the best previously known o p q time algorithm

a newton type midpoint method with high efficiency index abstract in this paper we present a newton type two step method to approximate a solution of a nonlinear equation in banach spaces we establish a semilocal convergence theorem under newton kantorovich type conditions both the convergence order and the efficiency index of the developed method are found the iterative procedure presented here is a simple modification of the newton kantorovich method however with the same number of function and derivative evaluations at each iteration it is improved in two important aspects firstly the convergence order is increased from 2 for the newton kantorovich method to 1 2 2 414 for the new method secondly the efficiency index convergence order per function evaluation is improved from 2 1 414 to 1 2 1 2 1 553 we illustrate some of our results with a numerical example

combinatorial properties of sequences defined by the billiard in paved triangles resume nous etudions certaines proprietes combinatoires de la dynamique symbolique du billard dans le triangle rectangle isocele et le demi triangle equilateral dans le cas du triangle rectangle isocele nous developpons un algorithme de construction des suites obtenues comme codage et nous calculons la complexite de ces suites lorsqu elles ne sont pas periodiques nous donnons des regles de construction des mots infinis qui codent les trajectoires de billard dans le demi triangle equilateral ceci nous a conduit a etablir un algorithme de construction du codage d un point sous une rotation munie d une partition en intervalles

some combinatorial properties of sturmian words abstract in this paper we give a characterization of finite sturmian words by palindrome words which generalizes a property of the fibonacci words we prove that the set st of finite sturmian words coincides with the set of the factors of all the words w such that w ab cxy with a b c palindromes x y a b and x y moreover using this result we prove that st is equal to the set of the factors of all words w having two periods p and q which are coprimes and such that w p q 2 several other combinatorial properties concerning special and bispecial elements of st are shown as a consequence we give a new and purely combinatorial proof of the enumeration formula of st

sturmian words structure combinatorics and their arithmetics abstract we prove some new results concerning the structure the combinatorics and the arithmetics of the set per of all the words w having two periods p and q p q which are coprimes and such that w p q 2 a basic theorem relating per with the set of finite standard sturmian words was proved in de luca and mignosi 1994 the main result of this paper is the following simple inductive definition of per the empty word belongs to per if w is an already constructed word of per then also aw and bw belong to per where denotes the operator of palindrome left closure i e it associates to each word u the smallest palindrome word u having u as a suffix we show that by this result one can construct in a simple way all finite and infinite standard sturmian words we prove also that up to the automorphism which interchanges the letter a with the letter b any element of per can be codified by the irreducible fraction p q this allows us to construct for any n 0 a natural bijection that we call farey correspondence of the set of the farey series of order n 1 and the set of special elements of length n of the set st of all finite sturmian words finally we introduce the concepts of farey tree and farey monoid this latter is obtained by defining a suitable product operation on the developments in continued fractions of the set of all irreducible fractions p q

quasi newton trust region algorithm for non smooth least squares problems1this work was supported by cnpq of brazil and the national natural science foundation of china 1 in this paper we present a quasi newton trust region algorithm for non smooth least squares problems which possess the smooth plus non smooth decomposition this method uses a smooth subproblem with second order information to approximate the locally lipschitzian function which is important to increase the convergence rate of the algorithm and deal with the large residual non smooth least squares problems the global and superlinear convergence of this algorithm are established

the mayer vietoris principle for grothendieck witt groups of schemes we prove localization and zariski mayer vietoris for higher gro thendieck witt groups alias hermitian k groups of schemes admitting an ample family of line bundles no assumption on the characteristic is needed and our schemes can be singular along the way we prove additivity fibration and approximation theorems for the hermitian k theory of exact categories with weak equivalences and duality

newton s method with a model trust region modification a modified newton method for unconstrained minimization is presented and analyzed the modification is based upon the model trust region approach this report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified newton iteration several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis very strong convergence results are presented concerning the minimization algorithm in particular the explicit use of second order information is justified by demonstrating that the iterates converge to a point which satisfies the second order necessary conditions for minimization with the exception of very pathological cases this occurs whenever the algorithm is applied to problems with continuous second partial derivatives

trust region algorithms for solving nonsmooth equations two globally convergent trust region algorithms are presented for solving nonsmooth equations where the functions are only locally lipschitzian the first algorithm is an extension of the classic levenberg marquardt method by approximating the locally lipschitzian function with a smooth function and using the derivative of the smooth function in the algorithm wherever a derivative is needed global convergence for this algorithm is established under a regular condition in the second algorithm successive smooth approximation functions and their derivatives are used global convergence for the second algorithm is established under mild assumptions both objective functions of subproblems of these two algorithms are quadratic functions

sturmian words lyndon words and trees abstract we prove some new combinatorial properties of the set per of all words w having two periods p and q which are coprimes and such that w p q 2 4 3 we show that aperb a b st lynd where st is the set of the finite factors of all infinite sturmian words and lynd is the set of the lyndon words on the alphabet a b it is also shown that aperb a b cp where cp is the set of christoffel primitive words such words can be defined in terms of the slope of the words and of their prefixes 1 from this result one can derive in a different way by using a theorem of borel and laubie that the elements of the set aperb are lyndon words we prove the following correspondence between the ratio p q of the periods p q p q of w per a a b and the slope w b 1 w a 1 of the corresponding christoffel primitive word awb if p q has the development in continued fractions 0 h 1 h n 1 h n 1 then has the development in continued fractions 0 h n h 2 h 1 1 this and other related results can be also derived by means of a theorem which relates the developments in continued fractions of the stern brocot and the raney numbers of a node in a complete binary tree however one needs some further results more precisely we label the binary tree with standard pairs standard tree christoffel pairs christoffel tree and the elements of per farey tree the main theorem is the following if the node w is labeled by the standard pair u v by the christoffel pair x y and by w per then uv wab xy awb the stern brocot number sb w is equal to the slope of the standard word uv and of the christoffel word xy while the raney number ra w is equal to the ratio of the minimal period of wa and the minimal period of wb some further auxiliary results are also derived

convergence analysis of some algorithms for solving nonsmooth equations this paper presents convergence analysis of some algorithms for solving systems of nonlinear equations defined by locally lipschitzian functions for the directional derivative based and the generalized jacobian based newton methods both the iterates and the corresponding function values are locally superlinearly convergent globally a limiting point of the iterate sequence generated by the damped directional derivative based newton method is a zero of the system if and only if the iterate sequence converges to this point and the stepsize eventually becomes one provided that the system is strongly bd regular and semismooth at this point in this case the convergence is superlinear a general attraction theorem is presented which can be applied to two algorithms proposed by han pang and rangaraj a hybrid method which is both globally convergent in the sense of finding a stationary point of the norm function of the system and locally quadratically convergent is also presented

parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed sphere high resolution and scalable parallel algorithms for the shallow water equations on the sphere are very important for modeling the global climate in this paper we introduce and study some highly scalable multilevel domain decomposition methods for the fully implicit solution of the nonlinear shallow water equations discretized with a second order well balanced finite volume method on the cubed sphere with the fully implicit approach the time step size is no longer limited by the stability condition and with the multilevel preconditioners good scalabilities are obtained on computers with a large number of processors the investigation focuses on the use of semismooth inexact newton method for the case with nonsmooth topography and the use of two and three level overlapping schwarz methods with different order of discretizations for the preconditioning of the jacobian systems we test the proposed algorithm for several benchmark cases and show numerically that this approach converges well with smooth and nonsmooth bottom topography and scales perfectly in terms of the strong scalability and reasonably well in terms of the weak scalability on machines with thousands and tens of thousands of processors

trust region algorithm for nonsmooth optimization minimization of a composite function h f x is considered here where f r n r m is a locally lipschitzian function and h r m r is a continuously differentiable convex function theory of trust region algorithm for nonsmooth optimization given by fletcher powell and yuan is extended to this case trust region algorithm and its global convergence are studied finally some applications on nonlinear and nonsmooth least squares problems are also given

nonmonotone trust region method for solving optimization problems in this paper a trust region tr method with nonmonotone technique for optimization is proposed we construct a new ratio of actual descent and predicted descent which is a simple and natural generalization of the modified armijo line search rule the paper exposes the relationship between the trust region method and line search approach since this method possesses the robust properties of trust region subproblem it is globally convergent although we employ the nonmonotone sequence of function values instead of the monotone sequence in addition the proof of convergence is obviously simpler than one of newton type method with nonmonotone line search finally applications of the nonmonotone tr algorithm to some optimization problems are discussed

normal maps inducted by linear transformations we study a certain piecewise linear manifold which we call the normal manifold associated with a polyhedral convex set and a family of continuous functions called normal maps that are induced on this manifold by continuous functions from rn to rn these normal maps occur frequently in optimization and equilibrium problems and the subclass of normal maps induced by linear transformations plays a key role our main result is that the normal map induced by a linear transformation is a lipschitzian homeomorphism if and only if the determinant of the map in each n cell of the normal manifold has the same nonzero sign

fine and wilf words for any periods ii given positive integers n and p 1 p r we establish a fast word combinatorial algorithm for constructing a word w w 1 w n of length n with periods p 1 p r and on the maximal number of distinct letters moreover we show that the constructed word which is unique up to word isomorphism is a pseudo palindrome i e it is a fixed point of an involutory antimorphism

graph connectivity partial words and a theorem of fine and wilf the problem of computing periods in words or finite sequences of symbols from a finite alphabet has important applications in several areas including data compression string searching and pattern matching algorithms the notion of period of a word is central in combinatorics on words there are many fundamental results on periods of words among them is the well known and basic periodicity result of fine and wilf which intuitively determines how far two periodic events have to match in order to guarantee a common period more precisely any word with length at least p q gcd p q having periods p and q has also period the greatest common divisor of p and q gcd p q moreover the bound p q gcd p q is optimal since counterexamples can be provided for words of smaller length partial words or finite sequences that may contain a number of do not know symbols or holes appear in natural ways in several areas of current interest such as molecular biology data communication dna computing etc any long enough partial word with h holes and having periods p q has also period gcd p q in this paper we give closed formulas for the optimal bounds l h p q in the case where p 2 and also in the case where q is large in addition we give upper bounds when q is small and h 3 4 5 6 or 7 no closed formulas for l h p q were known except for the cases where h 0 1 or 2 our proofs are based on connectivity in graphs associated with partial words a world wide web server interface has been established at www uncg edu mat research finewilf3 for automated use of a program which given a number of holes h and two periods p and q computes the optimal bound l h p q and an optimal word for that bound a partial word u with h holes of length l h p q 1 is optimal if p and q are periods of u but gcd p q is not a period of u

accelerating the convergence in the single source and multi source weber problems abstract the modified weiszfeld method y vardi c h zhang a modified weiszfeld algorithm for the fermat weber location problem mathematical programming 90 2001 559 566 is perhaps the most widely used algorithm for the single source weber problem swp in this paper in order to accelerate the efficiency for solving swp a new numerical method called weiszfeld newton method is developed by combining the modified weiszfeld method with the well known newton method global convergence of the new weiszfeld newton method is proved under mild assumptions for the multi source weber problem mwp a new location allocation heuristic cooper weiszfeld newton method is presented in the spirit of cooper algorithm l cooper heuristic methods for location allocation problems siam review 6 1964 37 53 using the new weiszfeld newton method in the location phase to locate facilities and adopting the nearest center reclassification algorithm ncra in the allocation phase to allocate the customers preliminary numerical results are reported to verify the evident effectiveness of weiszfeld newton method for swp and cooper weiszfeld newton method for mwp

sensitivity analysis of composite piecewise smooth equations this paper is a contribution to the sensitivity analysis of piecewise smooth equations a piecewise smooth function is a lipschitzian homeomorphism near a given point if and only if it is coherently oriented and has an invertible b derivative at this point we emphasise the role of functions of the typef g h whereg is piecewise smooth andh is smooth and present verifiable conditions which ensure that the functionf g tilde h is a lipschitzian homeomorphism near a given point for every tilde h sufficiently close toh with respect to thec1 topology

on a generalization of christoffel words epichristoffel words sturmian sequences are well known as the ones having minimal complexity over a 2 letter alphabet they are also the balanced sequences over a 2 letter alphabet and the sequences describing discrete lines they are famous and have been extensively studied since the 18th century one of the extensions of these sequences over a k letter alphabet with k 3 is the episturmian sequences which generalizes a construction of sturmian sequences using the palindromic closure operation there exists a finite version of the sturmian sequences called the christoffel words they have been known since the works of christoffel and have interested many mathematicians in this paper we introduce a generalization of christoffel words for an alphabet with 3 letters or more using the episturmian morphisms we call them the epichristoffel words we define this new class of finite words and show how some of the properties of the christoffel words can be generalized naturally or not for this class

conditions for convergence of trust region algorithms for nonsmooth optimization this paper discusses some properties of trust region algorithms for nonsmooth optimization the problem is expressed as the minimization of a functionh f x whereh is convex andf is a continuously differentiable mapping from to bounds for the second order derivative approximation matrices are discussed it is shown that powel s 7 8 results hold for nonsmooth optimization

on the convergence of modified newton methods for solving equations containing a non differentiable term we provide a semilocal convergence analysis for certain modified newton methods for solving equations containing a non differentiable term the sufficient convergence conditions of the corresponding newton methods are often taken as the sufficient conditions for the modified newton methods that is why the latter methods are not usually treated separately from the former however here we show that weaker conditions as well as a finer error analysis than before can be obtained for the convergence of modified newton methods numerical examples are also provided

on a semi smooth newton method and its globalization this paper addresses the globalization of the semi smooth newton method for non smooth equations f x 0 in mathbb r m with applications to complementarity and discretized l1 regularization problems assuming semi smoothness it is shown that super linearly convergent newton methods can be globalized if appropriate descent directions are used for the merit function f x 2 special attention is paid to directions obtained from the primal dual active set strategy

intersecting periodic words let a a 1 2v be a word which is a square and for which a 1 2u is also a square and a k 1 min k 2w 2v has period w where u

generalized pattern matching and periodicity under substring consistent equivalence relations let be a substring consistent equivalence relation scer on strings such that for any two strings x y x y implies that 1 x y and 2 x i j y i j for all 0 i j x examples of scer are parameterized pattern matching and order preserving pattern matching we present a generalized and efficient algorithm for pattern matching with scer also we show analogues of fine and wilf s periodicity lemma hold for scer

how many runs can a string contain given a string x x 1 n a repetition of period p in x is a substring u r x i 1 i rp p u r 2 where neither u x i 1 i p nor x i 1 i r 1 p 1 is a repetition the maximum number of repetitions in any string x is well known to be q nlogn a run or maximal periodicity of period p in x is a substring u rt x i 1 i rp t of x where u r is a repetition t a proper prefix of u and no repetition of period p begins at position i of x or ends at position i rp t 1 in 2000 kolpakov and kucherov showed that the maximum number r n of runs in any string x 1 n is o n but their proof was nonconstructive and provided no specific constant of proportionality at the same time they presented experimental data to prompt the conjecture r n

palindromes in circular words there is a very short and beautiful proof that the number of distinct non empty palindromes in a word of length n is at most n in this paper we show with a very complicated proof that the number of distinct non empty palindromes with length at most n in a circular word of length n is less than 5n 3 for n divisible by 3 we present circular words of length n containing 5n 3 2 distinct palindromes so the bound is almost sharp the paper finishes with some open problems

globally convergent newton methods for nonsmooth equations this paper presents some globally convergent descent methods for solving systems of nonlinear equations defined by locally lipschitzian functions these methods resemble the well known family of damped newton and gauss newton methods for solving systems of smooth equations they generalize some recent newton like methods for solving b differentiable equations which arise from various mathematical programs

global convergence on an active set sqp for inequality constrained optimization sequential quadratic programming sqp has been one of the most important methods for solving nonlinearly constrained optimization problems in this paper we present and study an active set sqp algorithm for inequality constrained optimization the active set technique is introduced which results in the size reduction of quadratic programming qp subproblems the algorithm is proved to be globally convergent thus the results show that the global convergence of sqp is still guaranteed by deleting some redundant constraints

nonmonotone adaptive trust region method for unconstrained optimization problems in this paper an adaptive trust region method with nonmonotone technique for unconstrained optimization problems is presented and analyzed the global and local convergence results of the algorithm are established numerical results show that the new method is efficient

generalised fine and wilf s theorem for arbitrary number of periods the well known fine and wilf s theorem for words states that if a word has two periods and its length is at least as long as the sum of the two periods minus their greatest common divisor then the word also has as period the greatest common divisor we generalise this result for an arbitrary number of periods our bound is strictly better in some cases than previous generalisations moreover we prove it optimal we show also that any extrenal word is unique up to letter renaming and give an algorithm to compute both the bound and a corresponding extremal word

conjugacy and episturmian morphisms episturmian morphisms generalize sturmian morphisms here we study some intrinsic properties of these morphisms invertibility presentation cancellativity unitarity characterization by conjugacy most of them are generalizations of known properties of sturmian morphisms but we present also some results on episturmian morphisms that have not already been stated in the particular case of sturmian morphisms characterization of the episturmian morphisms that preserve palindromes new algorithms to compute conjugates we also study the conjugation of morphisms in the general case and show that the monoid of invertible morphisms on an alphabet containing at least three letters is not finitely generated

on graphs of central episturmian words episturmian sequences are a natural extension of sturmian sequences to the case of finite alphabets of arbitrary cardinality in this paper we are interested in central episturmian words or simply epicentral words i e the palindromic prefixes of standard episturmian sequences an epicentral word admits a variety of faithful representations including as a directive word as a certain type of period vector as a parikh vector as a certain type of fine and wilf extremal word as a suitable modular matrix and as a labeled graph various interconnections between the different representations of an epicentral word are analyzed in particular we investigate the structure of the graphs of epicentral words proving some curious and surprising properties

global and superlinear convergence of inexact uzawa methods for saddle point problems with nondifferentiable mappings this paper investigates inexact uzawa methods for nonlinear saddle point problems we prove that the inexact uzawa method converges globally and superlinearly even if the derivative of the nonlinear mapping does not exist we show that the newton type decomposition method for saddle point problems is a special case of a newton uzawa method we discuss applications of inexact uzawa methods to separable convex programming problems and coupling of finite elements boundary elements for nonlinear interface problems

homotopy invariance of coherent witt groups we prove the following general homotopy invariance theorem for coherent witt groups let be a flat morphism of separated gorenstein schemes of finite krull dimension with affine fibers i e 1 y is an affine space over the residue field k y for all y y then the induced homomorphism of coherent witt groups is an isomorphism as an application we calculate the classical witt group of the affine hyperbolic sphere over a regular local ring

directional differentiability of metric projections onto moving sets at boundary points soient x y des espaces normes de dimension finie et x y une multifonction assignant a chaque xex un ensemble ferme x cy a x sont associees la fonction distance d x y r et la projection metrique a valeur d ensemble x y y on etudie les proprietes differentielles de au voisinage d un point x 0 y 0 avec y 0 point limite de l ensemble x 0

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

time stepping for three dimensional rigid body dynamics traditional methods for simulating rigid body dynamics involves determining the current contact arrangement e g each contact is either a rolling or sliding contact the development of this approach is most clearly seen in the work of haug et al mech machine theory 21 1986 401 425 and pfeiffer and glocker multibody dynamics with unilateral contacts wiley 1996 however there has been a controversy about the status of rigid body dynamics as a theory due to simple problems in the area which do not appear to have solutions the most famous if not the earliest is due to paul painleve c r acad sci paris 121 1895 112 115 recently a number of time stepping methods have been developed to overcome these difficulties these time stepping methods use integrals of the forces over time steps rather than the actual forces this allows impulsive forces without the need for a separate formulation or special procedures to cover this case the newest of these methods are developed in terms of complementarity problems the complementarity problems that define the time stepping procedure are solvable unlike previous methods for simulating rigid body dynamics with friction proof of the existence of solutions to the continuous problem can be shown in the sense of measure differential inclusions in terms of these methods in this paper a number of these variants will be discussed and their essential properties proven