a bundle bregman proximal method for convex nondifferentiable minimization by taking xk to be an approximate minimizer of where is a piecewise linear model of f constructed from accumulated subgradient linearizations of f dh is the d function of a generalized bregman function h and tk 0 convergence under implementable criteria is established by extending our recent framework of bregman proximal minimization which is of independent interest e g for nonquadratic multiplier methods for constrained minimization in particular we provide new insights into the convergence properties of bundle methods based on h 2

algebras of generalized quaternion type abstract we introduce and study the algebras of generalized quaternion type being natural generalizations of algebras which occurred in the study of blocks of group algebras with generalized quaternion defect groups we prove that all these algebras with 2 regular gabriel quivers are periodic algebras of period 4 and very specific deformations of the weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles the main result of the paper forms an important step towards the morita equivalence classification of all periodic symmetric tame algebras of non polynomial growth applying the main result we establish existence of wild periodic algebras of period 4 with arbitrary large number at least 4 of pairwise non isomorphic simple modules these wild periodic algebras arise as stable endomorphism rings of cluster tilting cohen macaulay modules over one dimensional hypersurface singularities

algebres graduees avec symetries abstract in this paper we define the notion of graded algebra with symmetries this notion is a generalization of the extended differential forms we prove that for a graded algebra with symmetries t we associate a subalgebra which generalizes the noncommutative differential forms using this algebra we can define the hochschild and cyclic homologies cup i products and the steenrod squares

blocks with trivial intersection defect groups we show that each block whose defect groups intersect pairwise trivially either has cyclic or generalised quaternion defect groups or is morita equivalent to one of a given list of blocks of central extensions of automorphism groups of non abelian simple groups in particular we classify all blocks of automorphism groups of non abelian simple groups whose defect groups are non cyclic and intersect pairwise trivially a consequence is that donovans conjecture holds for blocks whose defect groups intersect pairwise trivially

periodicity of self injective algebras of polynomial growth abstract let a be an indecomposable representation infinite tame finite dimensional algebra of polynomial growth over an algebraically closed field we prove that a is a periodic algebra with respect to action of the bimodule syzygy operator if and only if a is morita equivalent to a socle deformation of an orbit algebra b g where b is the repetitive category of a tubular algebra b and g is an admissible infinite cyclic automorphism group of b the main contribution in the paper is to prove the sufficiency part of this equivalence it is known that every orbit algebra b g of a tubular algebra b admits a presentation as an orbit algebra t b r h of an r fold trivial extension algebra t b r of b with respect to free action of a finite cyclic automorphism group h of t b r a significant part of the paper is devoted to explicit descriptions of the minimal projective bimodule resolutions of properly chosen ten exceptional self injective algebras of polynomial growth and showing that all of them are periodic algebras then we deduce the periodicity of all algebras socle equivalent to the orbit algebras b g t b r h of tubular algebras b from the periodicity of these ten exceptional algebras using invariance of periodicity for finite galois coverings and derived equivalences of algebras

a hybrid proximal extragradient self concordant primal barrier method for monotone variational inequalities this paper presents a hybrid proximal extragradient hpe self concordant primal barrier method for solving a monotone variational inequality over a closed convex set endowed with a self concordant barrier and with an underlying map that has lipschitz continuous derivative in contrast to the iteration of a previous method developed by the first and third authors that has to compute an approximate solution of a linearized variational inequality the one of the present method solves a simpler newton system of linear equations the method performs two types of iterations namely those that follow ever changing interior paths and those that correspond to large step hpe iterations due to its first order nature the present method is shown to have a better iteration complexity than its zeroth order counterparts such as korpelevich s algorithm and tseng s modified forward backward splitting method although its work per iteration is larger than the one for the latter methods

shuffle compatible permutation statistics abstract since the early work of richard stanley it has been observed that several permutation statistics have a remarkable property with respect to shuffles of permutations we formalize this notion of a shuffle compatible permutation statistic and introduce the shuffle algebra of a shuffle compatible permutation statistic which encodes the distribution of the statistic over shuffles of permutations this paper develops a theory of shuffle compatibility for descent statistics statistics that depend only on the descent set and length which has close connections to the theory of p partitions quasisymmetric functions and noncommutative symmetric functions we use our framework to prove that many descent statistics are shuffle compatible and to give explicit descriptions of their shuffle algebras thus unifying past results of stanley gessel stembridge aguiar bergeron nyman and petersen

nonlinear proximal point algorithms using bregman functions with applications to convex programming a bregman function is a strictly convex differentiable function that induces a well behaved distance measure or d function on euclidean space this paper shows that for every bregman function there exists a nonlinear version of the proximal point algorithm and presents an accompanying convergence theory applying this generalization of the proximal point algorithm to convex programming one obtains the d function proximal minimization algorithm of censor and zenios and a wide variety of new multiplier methods these multiplier methods are different from those studied by kort and bertsekas and include nonquadratic variations on the proximal method of multipliers

dualization of generalized equations of maximal monotone type this paper develops a simple duality framework for generalized equations defined by set valued mappings from a linear space to another the original problem is related to two auxiliary problems of the similar form corresponding to lagrangian and dual problems in the theory of convex programming as in convex programming the alternative formulations can be used to obtain information about a given problem and then used to solve it numerically in particular dualization can be used in deriving existence criteria for a given problem indirectly by considering one of the alternative formulations also a given problem can often be solved more easily by way of a dual method the strongest results of this paper concern monotone mappings in this context the duality framework yields several new criteria for maximal monotonicity of composite mappings these results are useful theoretically as well as in numerical solution of generalized equations the duality framework can also be used in problem decomposition since dualization can lead to reformulations to which operator splitting methods and other special methods can be applied

mac lane co homology of the second kind and wieferich primes abstract in this paper we investigate the connection between the mac lane co homology and wieferich primes in finite localizations of global number rings following the ideas of polishchuk positselski 29 we define the mac lane co homology of the second kind of an associative ring with a central element we compute these invariants for finite localizations of global number rings with an element w and obtain that the result is closely related to the wieferich primes to the base w in particular for a given non zero integer w the infiniteness of wieferich primes to the base w turns out to be equivalent to the following for any positive integer n we have h m l ii 0 z 1 n w q as an application of our technique we identify the ring structure on the mac lane cohomology of a global number ring and compute the adams operations introduced in this case by mccarthy 26 on its mac lane homology

the hochschild complex of a twisting cochain given any twisting cochain t c a where c is a connected coaugmented chain coalgebra and a is an augmented chain algebra over an arbitrary commutative ring r we construct a twisted extension of chain complexes full size image 1 k of which both the well known hochschild complex of an augmented associative algebra and the cohochschild complex of a coaugmented coassociative coalgebra 13 are special cases we therefore call h t the hochschild complex of the twisting cochain t we explore the extent of the naturality of the hochschild complex construction and apply the results of this exploration to determining conditions under which h t admits multiplicative or comultiplicative structure in particular we show that the hochschild complex on a chain hopf algebra always admits a natural comultiplication furthermore when a is a chain hopf algebra we determine conditions under which h t admits an rth power map extending the usual rth power map on a and lifting the identity on c as special cases we obtain that both the hochschild complex of any cocommutative hopf algebra and the cohochschild complex of the normalized chain complex of a simplicial double suspension admit power maps

derived equivalence classification of algebras of dihedral semidihedral and quaternion type abstract algebras of dihedral semidihedral and quaternion type were introduced by k erdmann as a generalization of blocks of finite groups of tame representation type in a series of papers erdmann gave a description of the morita equivalence classes of these algebras the aim of the present article is to present a classification of algebras of dihedral semidihedral and quaternion type up to derived equivalence as an application we can show that all basic algebras in erdmann s list are actually of tame representation type

eulerian idempotents and milnor moore theorem for certain non cocommutative hopf algebras abstract the purpose of this paper is to prove a milnor moore style theorem for a particular kind of non cocommutative hopf algebras the dendriform algebras a dendriform hopf algebra is a hopf algebra such that the product is the sum of two operations and verifying certain conditions between them and with the coproduct the role of lie algebras is played by brace algebras which are defined by n ary operations one for each n 2 satisfying some relations we show that a dendriform hopf algebra is isomorphic to the enveloping algebra of its brace algebra of primitive elements one of the ingredients of the proof is the construction of eulerian idempotents in this context

on the negative cyclic homology of shc algebras let mathbb k be a field of characteristic p geq 0 and s1 the unit circle we prove that the shc structure on a cochain algebra a da induces an associative product on the negative cyclic homology hc a when the cochain algebra a da is the algebra of normalized cochains of the simply connected topological space x with coefficients in mathbb k then hc a is isomorphic as a graded algebra to h s 1 lx mathbb k the s1 equivariant cohomology algebra of lx the free loop space of x we use the notion of shc formality introduced in topology 41 85 106 2002 to compute the s1 equivariant cohomology algebras of the free loop space of the complex projective space mathbb c p n when n 1 0 p and of the even spheres s2n when p 2

enriched p partitions and peak algebras abstract we develop a more general view of stembridge s enriched p partitions and use this theory to outline the structure of peak algebras for the symmetric group and the hyperoctahedral group initially we focus on commutative peak algebras spanned by sums of permutations with the same number of peaks where we consider several variations on the definition of peak whereas stembridge s enriched p partitions are related to quasisymmetric functions the dual coalgebra of solomon s type a descent algebra our generalized enriched p partitions are related to type b quasisymmetric functions the dual coalgebra of solomon s type b descent algebra using these functions we move on to explore non commutative peak algebras spanned by sums of permutations with the same set of peaks while some of these algebras have been studied before our approach gives explicit structure constants with a combinatorial description

backward forward algorithms for structured monotone inclusions in hilbert spaces abstract in this paper we study the backward forward algorithm as a splitting method to solve structured monotone inclusions and convex minimization problems in hilbert spaces it has a natural link with the forward backward algorithm and has the same computational complexity since it involves the same basic blocks but organized differently surprisingly enough this kind of iteration arises when studying the time discretization of the regularized newton method for maximally monotone operators first we show that these two methods enjoy remarkable involutive relations which go far beyond the evident inversion of the order in which the forward and backward steps are applied next we establish several convergence properties for both methods some of which were unknown even for the forward backward algorithm this brings further insight into this well known scheme finally we specialize our results to structured convex minimization problems the gradient projection algorithms and give a numerical illustration of theoretical interest

uniformity and inexact version of a proximal method for metrically regular mappings abstract we study stability properties of a proximal point algorithm for solving the inclusion 0 t x when t is a set valued mapping that is not necessarily monotone more precisely we show that the convergence of our algorithm is uniform in the sense that it is stable under small perturbations whenever the set valued mapping t is metrically regular at a given solution we present also an inexact proximal point method for strongly metrically subregular mappings and show that it is super linearly convergent to a solution to the inclusion 0 t x

a proximal method for composite minimization we consider minimization of functions that are compositions of convex or prox regular functions possibly extended valued with smooth vector functions a wide variety of important optimization problems fall into this framework we describe an algorithmic framework based on a subproblem constructed from a linearized approximation to the objective and a regularization term properties of local solutions of this subproblem underlie both a global convergence result and an identification property of the active manifold containing the solution of the original problem preliminary computational results on both convex and nonconvex examples are promising

new approach to the η proximal point algorithm and nonlinear variational inclusion problems abstract a new approach using the over relaxed proximal point algorithm in the context of solving a class of inclusion problems based on the notion of maximal monotonicity is developed and examined convergence analysis seems to be reasonable and finally some specializations are included furthermore the model developed in this communication seems to be appropriate to the yosida approximation in the sense that it can be applied to first order evolution equations inclusions as well

a practical general approximation criterion for methods of multipliers based on bregman distances this paper demonstrates that for generalized methods of multipliers for convex programming based on bregman distance kernels including the classical quadratic method of multipliers the minimization of the augmented lagrangian can be truncated using a simple generally implementable stopping criterion based only on the norms of the primal iterate and the gradient or a subgradient of the augmented lagrangian at that iterate previous results in this and related areas have required conditions that are much harder to verify such as e optimality with respect to the augmented lagrangian or strong conditions on the convex program to be solved here only existence of a kkt pair is required and the convergence properties of the exact form of the method are preserved the key new element in the analysis is the use of a full conjugate duality framework as opposed to mainly examining the action of the method on the standard dual function of the convex program an existence result for the iterates stronger than those possible for the exact form of the algorithm is also included

lagrangian duality and related multiplier methods for variational inequality problems we consider a new class of multiplier interior point methods for solving variational inequality problems with maximal monotone operators and explicit convex constraint inequalities developing a simple lagrangian duality scheme which is combined with the recent logarithmic quadratic proximal lqp theory introduced by the authors we derive three algorithms for solving the variational inequality vi problem this provides a natural extension of the methods of multipliers used in convex optimization and leads to smooth interior point multiplier algorithms we prove primal dual and primal dual convergence under very mild assumptions eliminating all the usual assumptions used until now in the literature for related algorithms applications to complementarity problems are also discussed

poincare koszul duality we prove a duality for factorization homology which generalizes both usual poincare duality for manifolds and koszul duality for mathcal e n algebras the duality has application to the hochschild homology of associative algebras and enveloping algebras of lie algebras we interpret our result at the level of topological quantum field theory

the generalized dowling lattices in this paper we study a new class of lattices called the generalized dowling lattices these lattices are parametrized by a positive integer n a finite group g and a meet sublattice k of the lattice of subgroups of g for an appropriate choice of k the generalized dowling lattice d0 g k agrees with the ordinary dowling lattice dn g for a different choice of k the generalized dowling lattices are the lattice of intersections of a set of subspaces in complex space the set of subspaces defined in terms of a representation of g generalizes the thick diagonal in en we compute the mobius function and characteristic polynomial of the lattice dn g k along with the homology of dn g k in terms of the homology of k we go on to compute the character of g wr sn acting on the homology of d g k this computation provides a nontrivial generalization of a result due to stanley concerning the character of s acting on the top homology of the partition lattice

the primal douglas rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem we apply the douglas rachford splitting algorithm to a class of multi valued equations consisting of the sum of two monotone mappings compared with the dual application of the same algorithm which is known as the alternating direction method of multipliers the primal application yields algorithms that seem somewhat involved however the resulting algorithms may be applied effectively to problems with certain special structure in particular we show that they can be used to derive decomposition algorithms for solving the variational inequality formulation of the traffic equilibrium problem

the cyclic homology of affine algebras in this paper we study the cyclic homology of affine algebras over a field of characteristic 0 we show that if a is such an algebra the inverse system hc 2m a s m decomposes in sufficiently large degrees into the direct h 2tta sum of the constant system with value mz inf and a system which is essentially zero the essentially zero component is the kernel of the loday quillen map l and the behavior of the restriction of s on it is closely related to the degeneracy of the spectral sequence associated with connes exact couple of a

nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems we consider projection algorithms for solving nonconvex feasibility problems in euclidean spaces of special interest are the method of alternating projections ap and the douglas rachford algorithm dr in the case of convex feasibility firm nonexpansiveness of projection mappings is a global property that yields global convergence of ap and for consistent problems dr a notion of local subfirm nonexpansiveness with respect to the intersection is introduced for consistent feasibility problems this together with a coercivity condition that relates to the regularity of the collection of sets at points in the intersection yields local linear convergence of ap for a wide class of nonconvex problems and even local linear convergence of nonconvex instances of the dr algorithm

an ellipsoidal branch and bound algorithm for global optimization a branch and bound algorithm is developed for global optimization branching in the algorithm is accomplished by subdividing the feasible set using ellipses lower bounds are obtained by replacing the concave part of the objective function by an affine underestimate a ball approximation algorithm obtained by generalizing of a scheme of lin and han is used to solve the convex relaxation of the original problem the ball approximation algorithm is compared to sedumi as well as to gradient projection algorithms using randomly generated test problems with a quadratic objective and ellipsoidal constraints

smooth methods of multipliers for complementarity problems this paper describes several methods for solving nonlinear complementarity problems a general duality framework for pairs of monotone operators is developed and then applied to the monotone complementarity problem obtaining primal dual and primal dual formulations we derive bregman function based generalized proximal algorithms for each of these formulations generating three classes of complementarity algorithms the primal class is well known the dual class is new and constitutes a general collection of methods of multipliers or augmented lagrangian methods for complementarity problems in a special case it corresponds to a class of variational inequality algorithms proposed by gabay by appropriate choice of bregman function the augmented lagrangian subproblem in these methods can be made continuously differentiable the primal dual class of methods is entirely new and combines the best theoretical features of the primal and dual methods some preliminary computation shows that this class of algorithms is effective at solving many of the standard complementarity test problems

a hybrid entropic proximal decomposition method with self adaptive strategy for solving variational inequality problems in this paper we propose a hybrid nonlinear decomposition projection method for solving a class of monotone variational inequality problems the algorithm utilizes the problems structure conductive to decomposition and a projection step to get the next iterate to make the method more practical we allow solving of the subproblems approximately and adopt the constructive accuracy criterion developed recently by solodov and svaiter for classical proximal point algorithm and by the author for generalized proximal point algorithm the fejer monotonicity to the solution set of the problem is obtained by only assuming the underlying mapping is monotone and the solution set is nonempty the parameter is allowed to vary in a larger interval than that of auslender and teboulle and we also propose some improved self adaptive strategies to choose the sequence of parameters which makes the algorithm more flexible

the peak algebra and the descent algebras of types b and d we show the existence of a unital subalgebra n of the symmetric group algebra linearly spanned by sums of permutations with a common peak set which we call the peak algebra we show that n is the image of the descent algebra of type b under the map to the descent algebra of type a which forgets the signs and also the image of the descent algebra of type d the algebra n contains a two sided ideal n which is defined in terms of interior peaks this object was introduced in previous work by nyman 2003 we find that it is the image of certain ideals of the descent algebras of types b and d we derive an exact sequence of the form 0 n n n 2 0 we obtain this and many other properties of the peak algebra and its peak ideal by first establishing analogous results for signed permutations and then forgetting the signs in particular we construct two new commutative semisimple subalgebras of the descent algebra of dimensions n and n 2 1 by grouping permutations according to their number of peaks or interior peaks we discuss the hopf algebraic structures that exist on the direct sums of the spaces n and n over n 0 and explain the connection with previous work of stembridge 1997 we also obtain new properties of his descents to peaks map and construct a type b analog

entropic proximal mappings with applications to nonlinear programming we introduce a family of new transforms based on imitating the proximal mapping of moreau and the associated moreau yosida proximal approximation of a function the transforms are constructed in terms of the a divergence functional a generalization of the relative entropy and of bregman s measure of distance an analogue of moreau s theorem associated with these entropy like distances is proved we show that the resulting entropic proximal maps share properties similar to the proximal mapping and provide a fairly general framework for constructing approximation and smoothing schemes for optimization problems applications of the results to the construction of generalized augmented lagrangians for nonlinear programs and the minimax problem are presented

a decomposition of solomon s descent algebra abstract a descent class in the symmetric group sn is the collection of permutations with a given descent set it was shown by l solomon j algebra41 1976 255 264 that the product in the group algebra q sn of two descent classes is a linear combination of descent classes thus descent classes generate a subalgebra of q sn we refer to it here as solomon s descent algebra and denote it by n this algebra is not semisimple but it has a faithul representation in terms of upper triangular matrices the main goal of this paper is a decomposition of its multiplicative structure it develops that n acts in a natural way on the so called lie monomials this action has a purely combinatorial description and is a crucial tool in the construction of a complete set of indecomposable representations of n in particular we obtain a natural basis of irreducible orthogonal idempotents indexed by partitions of n for the quotient n n natural bases of nilpotents and idempotents for the subspaces e ne for two arbitrary partitions and are also constructed and the dimensions of these spaces are given a combinatorial interpretation in terms of the so called decreasing factorization of an arbitary word into a product of lyndon words

derived equivalent tame blocks abstract in this article we provide derived equivalences between several blocks of tame representation type based on erdmann s work on morita equivalence classes of tame blocks we obtain a classification of tame blocks up to derived equivalence as in erdmann s work in the case of two simple modules our classification is only complete up to scalars occurring in certain relations

convergence analysis of a proximal like minimization algorithm using bregman functions an alternative convergence proof of a proximal like minimization algorithm using bregman functions recently proposed by censor and zenios is presented the analysis allows the establishment of a global convergence rate of the algorithm expressed in terms of function values

a multiplication in cyclic homology we define a multiplication on the cyclic homology of a commutative cocommutative bialgebra h with superproduct in the case when h is a field of characteristic zero the cyclic homology becomes a polynomial algebra in one generator the loday quillen multiplication is trivial in that case in this paper we define an associative multiplication on the cyclic homology of certain commutative algebras h the definition is based on the cartesian product of sets instead of the shuffle product as in the case of lq and ga when h contains q our product is compatible with the hodge decomposition of hc h so it has the form hc n h hc j m h hc n m h the existence of this multiplication in the case h k is classical since it is just given by the tensor product of complex line bundle however its significance came to our attention in joint work with john klein as a consequence of our study of fiberwise morse theory on circle bundles ik and in other joint works with r penner and r hain by doing morse theory on circles john klein and i realized that there was a rationally nontrivial associative multiplication on the cyclic homology of the integral group ring on any cyclic group and that it had important consequences for pseudoisotopy theory this will be explained in a later paper in this paper we show that this multiplication in cyclic homotopy is defined first in the case when the algebra is h km k m where m is the underlying additive group of a ring then in the case when h is a hopf algebra with superproduct in the sense of gaucher ga and finally in the more general case of any algebra example 12 4 in fact we do not need additive inverses in m nor do we need an antipode for h so we can take m to be a monoid and h to be a bialgebra when h k i e m 1 the cyclic homology becomes a divided power algebra which is of course isomorphic to a polynomial algebra in one generator if k is a field of characteristic zero we assume throughout the paper that k is a commutative ring with 1 and that all tensor products are taken over k this includes those tensor products which appear in the definition of cyclic homology we also use connes original definition that a cyclic object in a category c is a covariant functor c where is connes cyclic category since this is the same as a contravariant functor c an outline of the paper is as follows in the first section we give a topological definition of the multiplication in hc km the construction is so elementary that received by the editors april 14 1994 1991 mathematics subject classification primary 18g60 secondary 16w30 this research was supported by nsf grant no dms 90 02512 c 1999 american mathematical society

inexact variants of the proximal point algorithm without monotonicity this paper studies convergence properties of inexact variants of the proximal point algorithm when applied to a certain class of nonmonotone mappings the presented algorithms allow for constant relative errors in the line of the recently proposed hybrid proximal extragradient algorithm the main convergence result extends a recent work of the second author where exact solutions for the proximal subproblems were required we also show that the linear convergence property is preserved in the case when the inverse of the operator is locally lipschitz continuous near the origin as an application we give a convergence analysis for an inexact version of the proximal method of multipliers for a rather general family of problems which includes variational inequalities and constrained optimization problems

a monotone skew splitting model for composite monotone inclusions in duality the principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally monotone operator and a linear skew adjoint operator an algorithmic framework is developed for solving this generic problem in a hilbert space setting new primal dual splitting algorithms are derived from this framework for inclusions involving composite monotone operators and convergence results are established these algorithms draw their simplicity and efficacy from the fact that they operate in a fully decomposed fashion in the sense that the monotone operators and the linear transformations involved are activated separately at each iteration comparisons with existing methods are made and applications to composite variational problems are demonstrated

proximal methods for cohypomonotone operators conditions are given for the viability and the weak convergence of an inexact relaxed proximal point algorithm for finding a common zero of countably many cohypomonotone operators in a hilbert space in turn new convergence results are obtained for an extended version of the proximal method of multipliers in nonlinear programming

on the range of the douglas rachford operator the problem of finding a minimizer of the sum of two convex functions or more generally that of finding a zero of the sum of two maximally monotone operators is of central importance in variational analysis perhaps the most popular method of solving this problem is the douglas rachford splitting method surprisingly little is known about the range of the douglas rachford operator in this paper we set out to study this range systematically we prove that for 3 monotone operators a very pleasing formula can be found that reveals the range to be nearly equal to a simple set involving the domains and ranges of the underlying operators a similar formula holds for the range of the corresponding displacement mapping we discuss applications to subdifferential operators to the infimal displacement vector and to firmly nonexpansive mappings various examples and counterexamples are presented including some concerning the celebrated brezis haraux theorem

a generalized proximal point algorithm for the variational inequality problem in a hilbert space we consider a generalized proximal point method for solving variational inequality problems with monotone operators in a hilbert space it differs from the classical proximal point method as discussed by rockafellar for the problem of finding zeroes of monotone operators in the use of generalized distances called bregman distances instead of the euclidean one these distances play not only a regularization role but also a penalization one forcing the sequence generated by the method to remain in the interior of the feasible set so that the method becomes an interior point one under appropriate assumptions on the bregman distance and the monotone operator we prove that the sequence converges weakly if and only if the problem has solutions in which case the weak limit is a solution if the problem does not have solutions then the sequence is unbounded we extend similar previous results for the proximal point method with bregman distances which dealt only with the finite dimensional case and which applied only to convex optimization problems or to finding zeroes of monotone operators which are particular cases of variational inequality problems

proximal methods in reflexive banach spaces without monotonicity abstract we introduce the concept of hypomonotone point to set operators in banach spaces with respect to a regularizing function this notion coincides with the one given by rockafellar and wets in hilbertian spaces when the regularizing function is the square of the norm we study the associated proximal mapping which leads to a hybrid proximal extragradient and proximal projection methods for nonmonotone operators in reflexive banach spaces these methods allow for inexact solution of the proximal subproblems with relative error criteria we then consider the notion of local hypomonotonicity and propose localized versions of the algorithms which are locally convergent

multibasic eulerian polynomials eulerian polynomials with several bases are defined their combinatorial interpretations are given as well as congruence properties modulo some ideals generated by cyclotomic polynomials

derived equivalences for tame weakly symmetric algebras having only periodic modules abstract recently a classification up to morita equivalence of all weakly symmetric algebras which have tame representation type simply connected galois coverings and all of whose modules are periodic equivalently the stable auslander reiten quiver consist only of tubes has been completed in j bialkowski a skowronski on tame weakly symmetric algebras having only periodic modules arch math to appear we classify in this paper these algebras up to derived equivalence and give a set of representatives for the derived equivalence classes

infinitesimal cohomology and the chern character to negative cyclic homology there is a chern character from k theory to negative cyclic homology we show that it preserves the decomposition coming from adams operations at least in characteristic zero

modules and morita theorem for operads associative rings a b are called morita equivalent when the categories of left modules over them are equivalent we call two classical linear operads p q morita equivalent if the categories of algebras over them are equivalent we transport a part of morita theory to the operadic context by studying modules over operads as an application of this philosophy we consider an operadic version of the sheaf of linear differential operators on a super manifold m and give a comparison theorem between algebras over this sheaf on m and m red

a class of inexact variable metric proximal point algorithms for the problem of solving maximal monotone inclusions we present a rather general class of algorithms which contains hybrid inexact proximal point methods as a special case and allows for the use of a variable metric in subproblems the global convergence and local linear rate of convergence are established under standard assumptions we demonstrate the advantage of variable metric implementation in the case of solving systems of smooth monotone equations by the proximal newton method

a primal dual splitting algorithm for finding zeros of sums of maximal monotone operators we consider the primal problem of finding the zeros of the sum of a maximal monotone operator and the composition of another maximal monotone operator with a linear continuous operator by formulat

generalized eckstein bertsekas proximal point algorithm based on a maximal monotonicity design a general design for the eckstein bertsekas proximal point algorithm using the notion of the a maximal monotonicity is developed convergence analysis for the generalized eckstein bertsekas proximal point algorithm in the context of solving a class of nonlinear inclusion problems is explored some auxiliary results of interest involving a maximal monotone mappings are also included the obtained results generalize investigations on general maximal monotonicity and beyond

hochschild cohomology of tame blocks abstract we study the additive structure of hochschild cohomology for blocks of modular group algebras of tame representation type we give explicit formulae for the dimensions of the cohomology groups and compute the poincare series of the hochschild cohomology ring for all tame blocks having one or three simple modules

an interior point method with bregman functions for the variational inequality problem with paramonotone operators we present an algorithm for the variational inequality problem on convex sets with nonempty interior the use of bregman functions whose zone is the convex set allows for the generation of a sequence contained in the interior without taking explicitly into account the constraints which define the convex set we establish full convergence to a solution with minimal conditions upon the monotone operatorf weaker than strong monotonicity or lipschitz continuity for instance and including cases where the solution needs not be unique we apply our algorithm to several relevant classes of convex sets including orthants boxes polyhedra and balls for which bregman functions are presented which give rise to explicit iteration formulae up to the determination of two scalar stepsizes which can be found through finite search procedures 1998 the mathematical programming society inc published by elsevier science b v