on identification of active constraints ii the nonconvex case in this paper the results of burke and more 5 on the identification of active constraints are extended to the nonconvex constrained nonlinear programming problem the approach is motivated by the geometric structure of a certain polyhedral convex linearization of the constraint region at each iteration as in burke and more 5 questions of constraint identification are couched in terms of the faces of these polyhedra the main result employs a nondegeneracy condition due to dunn 7 and the linear independence condition to obtain a characterization of those algorithms that identify the optimal active constraints in a finite number of iterations the role of the linear independence condition is carefully examined and it is argued that it is required within the context of a first order theory of constraint identification in conclusion the characterization theorem is applied to the wilson han powell sequential quadratic programming algorithm j optim theory appl 22 1977 pp 297 309 proceedin

nonlinear programming algorithms using trust regions and augmented lagrangians with nonmonotone penalty parameters the strategy for obtaining global convergence is based on the trust region approach the merit function is a type of augmented lagrangian a new updating scheme is introduced for the penalty parameter by means of which monotone increase is not necessary global convergence results are proved and numerical experiments are presented

a nonmonotone trust region algorithm with nonmonotone penalty parameters for constrained optimization in this paper we present a nonmonotone trust region algorithm with nonmonotone penalty parameters for the solution of optimization problems with nonlinear equality constraints and bound constraints the proposed algorithm combines an sqp approach with a trust region strategy to globalize the process each step is obtained through the computation of a normal step to reduce infeasibility and a tangential step to decrease some merit function the algorithm makes use of an augmented lagrangian function as merit function and allows the value of this merit function and the penalty parameter involved in it to decrease non monotonically the global convergence theory for the proposed algorithm is developed without regularity assumption and shows that any limit point of the sequence generated by the algorithm is a stationary point while at least one limit point under the suitable assumptions is a substationary point and a stationary point if it is feasible some preliminary numerical experiments are also reported

large 2 groups of automorphisms of algebraic curves over a field of characteristic 2 abstract let s be a 2 subgroup of the k automorphism group aut x of an algebraic curve x of genus g x defined over an algebraically closed field k of characteristic 2 it is known that s may be quite large compared to the classical hurwitz bound 84 g x 1 however if s fixes no point then the size of s is smaller than or equal to 4 g x 1 in this paper we investigate algebraic curves x with a 2 subgroup s of aut x having the following properties i s 8 and s 2 g x 1 ii s fixes no point on x theorem 1 2 shows that x is a general curve and that either s 4 g x 1 or s 2 g x 2 or for every involution u z s the quotient curve x u inherits the above properties that is it has genus 2 and its automorphism group s u still has properties i and ii in the first two cases s is completely determined we also give examples illustrating our results in particular for every g 2 h 1 9 we exhibit a general bielliptic curve x of genus g whose k automorphism group has a dihedral 2 subgroup s of order 4 g 1 that fixes no point in x

spectral properties of a matrix of redheffer abstract define n n matrices d n d ij and c n c ij by d ij 1 if i j 0 otherwise and c n 0 1 1 1 t 1 0 0 0 let a n d n c n the matrix is of number theoretic significance because det a n m n is mertens function we give a simplified derivation of the characteristic polynomial of a n give precise asymptotic estimates for its two large eigenvalues and use rouche s theorem to significantly improve a previous bound on its small eigenvalues finally we present some attractive conjectures about these small eigenvalues based on numerical evidence

subdifferential regularities of perturbed distance functions outside the target set in banach spaces abstract this paper is devoted to study the frechet and proximal regularities at points outside the target set of perturbed distance functions d s j determined by a closed subset s and a lipschitz function j also we provide some important results on the frechet proximal and clarke subdifferentials of d s j at those points in banach spaces

the complete list of genera of quotients of the fq2 maximal hermitian curve for q 1 mod 4 abstract let f q 2 be the finite field with q 2 elements most of the known f q 2 maximal curves arise as quotient curves of the f q 2 maximal hermitian curve h q after a seminal paper by garcia stichtenoth and xing many papers have provided genera of quotients of h q but their complete determination is a challenging open problem in this paper we determine completely the spectrum of genera of quotients of h q for any q 1 mod 4

a new family of maximal curves over a finite field it has been known for a long time that the deligne lusztig curves associated to the algebraic groups of type 2a 2 2b 2 and 2g 2 defined over the finite field mathbb f n all have the maximum number of mathbb f n rational points allowed by the weil explicit formulas and that these curves are mathbb f q 2 maximal curves over infinitely many algebraic extensions mathbb f q 2 of mathbb f n serre showed that an mathbb f q 2 rational curve which is mathbb f q 2 covered by an mathbb f q 2 maximal curve is also mathbb f q 2 maximal this has posed the problem of the existence of mathbb f q 2 maximal curves other than the deligne lusztig curves and their mathbb f q 2 subcovers see for instance garcia on curves with many rational points over finite fields in finite fields with applications to coding theory cryptography and related areas pp 152 163 springer berlin 2002 and garcia and stichtenoth a maximal curve which is not a galois subcover of the hermitan curve bull braz math soc n s 37 139 152 2006 in this paper a positive answer to this problem is obtained for every q n 3 with n p r 2 p 2 prime we give a simple explicit construction of an mathbb f q 2 maximal curve mathcal x that is not mathbb f q 2 covered by any mathbb f q 2 maximal deligne lusztig curve furthermore the mathbb f q 2 automorphism group aut mathcal x has size n 3 n 3 1 n 2 1 n 2 n 1 interestingly mathcal x has a very large mathbb f q 2 automorphism group with respect to its genus g frac 1 2 n 3 1 n 2 2 1

automorphisms of harbater katz gabber curves let k be a perfect field of characteristic p 0 and let g be a finite group we consider the pointed g curves over k associated by harbater katz and gabber to faithful actions of g on k t over k we use such hkg g curves to classify the automorphisms of k t of p power order that can be expressed by particularly explicit formulas namely those mapping t to a power series lying in a mathbb z p mathbb z artin schreier extension of k t in addition we give necessary and sufficient criteria to decide when an hkg g curve with an action of a larger finite group j is also an hkg j curve

on the convergence of a new trust region algorithm in this paper we present a new trust region algorithm for general nonlinear constrained optimization problems the algorithm is based on the l infty exact penalty function under very mild conditions global convergence results for the algorithm are given local convergence properties are also studied it is shown that the penalty parameter generated by the algorithm will be eventually not less than the l 1 norm of the lagrange multipliers at the accumulation point it is proved that the method is equivalent to the sequential quadratic programming method for all large k hence superlinearly convergent results of the sqp method can be applied numerical results are also reported

on the spectral radius of a 0 1 matrix related to merten s function abstract define n n matrices dn dij and cn cij by dij 1 if i j 0 otherwise and cn 0 1 1 1 t 1 0 0 0 let an dn cn we use the directed graph of an in to obtain the characteristic polynomial of an then we show that all but log2n 1 of the eigenvalues of an are equal to 1 and that an is asymptotically equal to n as n

a sequential quadratic programming method for potentially infeasible mathematical programs abstract the paper describes a modification to the wilson han powell sequential quadratic programming technique that is applicable to potentially infeasible nonlinear programs the method is designed to locate stationary points of a nonlinear program in a generalized sense definition 2 8 these stationary points include the familiar kuhn tucker and fritz john points but also include what we call external and strong external stationary points the external and strong external stationary points are not feasible thus the problem may be infeasible and yet have stationary points loosely speaking an external stationary point is one that satisfies a certain first order necessary optimality condition for being as close to feasibility as possible the proposed technique is similar to those described by j v burke and s p han a modified sequential quadratic programming method manuscript and m sahba j optim theory appl 52 1987 291 309 however it is shown to possess substantially enhanced stability properties the global convergence properties of the method are described along with some continuity results for the quadratic programming subproblems

riordan group involutions we study involutions in the riordan group especially those with combinatorial meaning we give a new determinantal criterion for a matrix to be a riordan involution and examine several classes of examples a complete characterization of involutions in the appell subgroup is developed in another direction we find several examples that generalize the rna matrix but are of independent interest

binomial determinants paths and hook length formulae abstract we give a combinatorial interpretation for any minor or binomial determinant of the matrix of binomial coefficients this interpretation involves configurations of nonintersecting paths and is related to young tableaux and hook length formulae

a simple feasible sqp algorithm for inequality constrained optimization in this paper an sqp method generating feasible iterates is presented to solve the nonlinear inequality constrained optimization problems a new modified method which ensures the global and superlinear convergence is proposed by solving systems of linear equation instead of qp subproblems and linear squares problems here the search direction is a suitable combination of a descent direction a feasible direction and a second order revised direction the theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions

large p groups of automorphisms of algebraic curves in characteristic p abstract let s be a p subgroup of the k automorphism group aut x of an algebraic curve x of genus g 2 and p rank defined over an algebraically closed field k of characteristic p 3 nakajima 27 proved that if 2 then s p p 2 g 1 if equality holds x is a nakajima extremal curve we prove that if s p 2 p 2 p 1 g 1 then one of the following cases occurs i 0 and the extension k x k x s completely ramifies at a unique place and does not ramify elsewhere ii s p and x is an ordinary curve of genus g p 1 iii x is an ordinary nakajima extremal curve and k x is an unramified galois extension of a function field of a curve given in ii iii x is an ordinary nakajima extremal curve and k x is an unramified galois extension of a function field of a curve given in ii there are exactly p 1 subgroups m of s such that k x k x m is such a galois extension moreover if some of them is an abelian extension then s has maximal nilpotency class the full k automorphism group of any nakajima extremal curve is determined and several infinite families of nakajima extremal curves are constructed by using their pro p fundamental groups

algebraic curves with many automorphisms abstract let x be a projective geometrically irreducible non singular algebraic curve of genus g 2 defined over an algebraically closed field k of odd characteristic p let aut x be the group of all automorphisms of x which fix k element wise it is known that if aut x 8 g 3 then the p rank equivalently the hasse witt invariant of x is zero this raises the problem of determining the minimum value function f g such that whenever aut x f g then x has zero p rank for even g we prove that f g 900 g 2 the odd genus case appears to be much more difficult although for any genus g 2 if aut x has a solvable subgroup g such that g 252 g 2 then x has zero p rank and g fixes a point of x our proofs use the hurwitz genus formula and the deuring shafarevich formula together with a few deep results from group theory characterizing finite simple groups whose sylow 2 subgroups have a cyclic subgroup of index 2 we also point out some connections with the abhyankar conjecture and the katz gabber covers

a q analogue of the riordan group abstract the riordan group consisting of riordan matrices shows up naturally in a variety of combinatorial settings in this paper we define a q riordan matrix to be a q analogue of the exponential riordan matrix by using the eulerian generating functions of the form n 0 f n z n n q we first prove that the set of q riordan matrices forms a loop a quasigroup with an identity element and find its loop structures next it is shown that q riordan matrices associated to the counting functions may be applied to the enumeration problem on set partitions by block inversions this notion leads us to find q analogues of the composition formula and the exponential formula respectively

epi convergent smoothing with applications to convex composite functions smoothing methods have become part of the standard tool set for the study and solution of nondifferentiable and constrained optimization problems as well as a range of other variational and equilibrium problems in this note we synthesize and extend recent results due to beck and teboulle on infimal convolution smoothing for convex functions with those of x chen on gradient consistency for nonconvex functions we use epi convergence techniques to define a notion of epi smoothing that allows us to tap into the rich variational structure of the subdifferential calculus for nonsmooth nonconvex and nonfinite valued functions as an illustration of the versatility and range of epi smoothing techniques the results are applied to the general constrained optimization for which nonlinear programming is a special case

new q laguerre polynomials having factorized permutation interpretations abstract in this paper we generalize the laguerre polynomials in terms of q analogue for riordan matrices to be more specific for n 0 we introduce new q laguerre polynomials l n x q by defining the eulerian generating function for l n x q as j 0 1 1 q j 1 z e q x z 1 z interestingly it turns out that l n x q have combinatorial descriptions in the aspect of the inversions of factorized permutations and q rook numbers we locate their zeros and develop their algebraic properties as well

some combinatorial applications of the q riordan matrix abstract recently the authors developed a q analogue for riordan matrices by means of eulerian generating functions of the form g z n 0 g n z n n q where n q is the q factorial we apply this concept to give q analogues of some familiar objects from the set partitions with double restrictions on blocks namely the r s bessel numbers of both types by setting r 0 and letting s these numbers may be reduced to the q stirling numbers of both kinds several algebraic formulas for the q analogues are also derived using combinatorial methods together with the concept of q riordan matrices in particular q analogues of the classical bessel numbers of both kinds and their combinatorial interpretations are obtained

mertens equimodular matrices of redheffer type abstract asymptotic behavior of the mertens function m n k 0 n k which is equal to the determinant of the n n redheffer matrix is known to be closely related to the riemann hypothesis an infinite matrix whose nth leading principal minor is equal to m n for all n 1 is called a mertens equimodular matrix we use riordan matrices to find a large class of mertens equimodular matrices each element of which is called by us a riordan redheffer matrix briefly an r r matrix we also give the generating function for the characteristic polynomials of r r matrices as a result we introduce several examples of r r matrices that reveal interesting spectral properties further we pose two conjectures on the eigenvalues of those r r matrices finally we find a sufficient condition for the riemann hypothesis using the smallest singular value of a r r matrix

an augmented lagrangian function with improved exactness properties in this paper we introduce a new exact augmented lagrangian function for the solution of general nonlinear programming problems for this lagrangian function a complete equivalence between its unconstrained minimization on an open set and the solution of the original constrained problem can be established under mild assumptions and without requiring the boundedness of the feasible set of the constrained problem moreover we describe an unconstrained algorithmic model which is globally convergent toward kkt pairs of the original constrained problem the algorithmic model can be endowed with a superlinear rate of convergence by a proper choice of the search direction in the unconstrained minimization without requiring strict complementarity

on using the elastic mode in nonlinear programming approaches to mathematical programs with complementarity constraints we investigate the possibility of solving mathematical programs with complementarity constraints mpccs using algorithms and procedures of smooth nonlinear programming although mpccs do not satisfy a constraint qualification we establish sufficient conditions for their lagrange multiplier set to be nonempty mpccs that have nonempty lagrange multiplier sets and satisfy the quadratic growth condition can be approached by the elastic mode with a bounded penalty parameter in this context the elastic mode transforms mpcc into a nonlinear program with additional variables that has an isolated stationary point and local minimum at the solution of the original problem which in turn makes it approachable by sequential quadratic programming sqp algorithms one such algorithm is shown to achieve local linear convergence once the problem is relaxed under stronger conditions we also prove superlinear convergence to the solution of an mpcc using an adaptive elastic mode approach for an sqp algorithm recently analyzed in an mpcc context in r fletcher s leyffer s sholtes and d ralph local convergence of sqp methods for mathematical programs with equilibrium constraints tech report na 210 university of dundee dundee uk 2002 our assumptions are more general since we do not use a critical assumption from that reference in addition we show that the elastic parameter update rule will not interfere locally with the superlinear convergence once the penalty parameter is appropriately chosen

an inequality constrained nonlinear kalman bucy smoother by interior point likelihood maximization kalman bucy smoothers are often used to estimate the state variables as a function of time in a system with stochastic dynamics and measurement noise this is accomplished using an algorithm for which the number of numerical operations grows linearly with the number of time points all of the randomness in the model is assumed to be gaussian including other available information for example a bound on one of the state variables is non trivial because it does not fit into the standard kalman bucy smoother algorithm in this paper we present an interior point method that maximizes the likelihood with respect to the sequence of state vectors satisfying inequality constraints the method obtains the same decomposition that is normally obtained for the unconstrained kalman bucy smoother hence the resulting number of operations grows linearly with the number of time points we present two algorithms the first is for the affine case and the second is for the nonlinear case neither algorithm requires the optimization to start at a feasible sequence of state vector values both the unconstrained affine and unconstrained nonlinear kalman bucy smoother are special cases of the class of problems that can be handled by these algorithms

the nonlinear programming method of wilson han and powell with an augmented lagrangian type line search function the paper represents an outcome of an extensive comparative study of nonlinear optimization algorithms this study indicates that quadratic approximation methods which are characterized by solving a sequence of quadratic subproblems recursively belong to the most efficient and reliable nonlinear programming algorithms available at present the purpose of this paper is to analyse the theoretical convergence properties and to investigate the numerical performance in more detail in part 1 the exactl 1 penalty function of han and powell is replaced by a differentiable augmented lagrange function for the line search computation to the able to prove the global convergence and to show that the steplength one is chosen in the neighbourhood of a solution in part 2 the quadratic subproblem is exchanged by a linear least squares problem to improve the efficiency and to test the dependence of the performance from different solution methods for the quadratic or least squares subproblems

finite and infinite dimensional lie group structures on riordan groups abstract we introduce a frechet lie group structure on the riordan group we give a description of the corresponding lie algebra as a vector space of infinite lower triangular matrices we describe a natural linear action induced on the frechet space k n by any element in the lie algebra we relate this to a certain family of bivariate linear partial differential equations we obtain the solutions of such equations using one parameter groups in the riordan group we show how a particular semidirect product decomposition in the riordan group is reflected in the lie algebra we study the stabilizer of a formal power series under the action induced by riordan matrices we get stabilizers in the fraction field k x using bi infinite representations we provide some examples the main tool to get our results is the paper 18 where the riordan group was described using inverse sequences of groups of finite matrices

a sequential quadratic optimization algorithm with rapid infeasibility detection we present a sequential quadratic optimization sqo algorithm for nonlinear constrained optimization the method attains all of the strong global and fast local convergence guarantees of classical sqo methods but has the important additional feature that fast local convergence is guaranteed when the algorithm is employed to solve infeasible instances a two phase strategy carefully constructed parameter updates and a line search are employed to promote such convergence the first phase subproblem determines the reduction that can be obtained in a local model of an infeasibility measure when the objective function is ignored the second phase subproblem then seeks to minimize a local model of the objective while ensuring that the resulting search direction attains a reduction in the local model of the infeasibility measure that is proportional to that attained in the first phase the subproblem formulations and parameter updates ensure that near an optimal solution the algorithm reduces to a classica

a variant of sqp method for inequality constrained optimization and its global convergence in this paper a variant of sqp method for solving inequality constrained optimization is presented this method uses a modified qp subproblem to generate a descent direction as each iteration and can overcome the possible difficulties that the qp subproblem of the standard sqp method is inconsistency furthermore the method can start with an infeasible initial point under mild conditions we prove that the algorithm either terminates as kkt point within finite steps or generates an infinite sequence whose accumulation point is a kkt point or satisfies certain first order necessary condition finally preliminary numerical results are reported

congruence properties of q analogs abstract using group actions and generating functions we derive various arithmetic properties of the q binomial coefficients and q stirling numbers these include recurrence relations and computation of residues modulo a cyclotomic polynomial we also obtain periodicity and non periodicity results

a q analogue of mahler expansions i abstract we examine a q analogue of mahler expansions for continuous functions in p adic analysis replacing binomial coefficient polynomials x n with a q analogue x n q for a p adic variable q with q 1 p q 1 and we consider the p adic q gamma function p q of koblitz relative to its q mahler expansion

a feasible sqp method for nonlinear programming in this paper a new sqp algorithm is presented to solve the general nonlinear programs with mixed equality and inequality constraints quoted from p spellucci see 9 this method maybe be named sequential equality constrained quadratic programming secqp algorithm per single iteration based on an active set strategy see 9 this secqp algorithm requires only to solve equality constrained quadratic programming subproblems or system of linear equations the theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions

a global convergence theory for dennis el alem and maciel s class of trust region algorithms for constrained optimization without assuming regularity this work presents a convergence theory for dennis el alem and maciel s class of trust region based algorithms for solving the smooth nonlinear programming problem with equality constraints the results are proved under very mild conditions on the quasi normal and tangential components of the trial steps the lagrange multiplier estimates and the hessian estimates are assumed to be bounded no regularity assumption is made in particular linear independence of the gradients of the constraints is not assumed the theory proves global convergence for the class in particular it shows that a subsequence of the iteration sequence satisfies one of four types of mayer bliss stationary conditions in the limit

algebraic curves with a large non tame automorphism group fixing no point let k be an algebraically closed field of characteristic p 0 and let x be a curve over k of genus g 2 assume that the automorphism group aut x of x over k fixes no point of x the following result is proven if there is a point p on x whose stabilizer in aut x contains a p subgroup of order greater than gp p 1 then x is birationally equivalent over k to one of the irreducible plane curves ii iii iv v listed in the introduction

a robust algorithm for optimization with general equality and inequality constraints an algorithm for general nonlinearly constrained optimization is presented which solves an unconstrained piecewise quadratic subproblem and a quadratic programming subproblem at each iterate the algorithm is robust since it can circumvent the difficulties associated with the possible inconsistency of qp subproblem of the original sqp method moreover the algorithm can converge to a point which satisfies a certain first order necessary optimality condition even when the original problem is itself infeasible which is a feature of burke and han s methods math programming 43 1989 pp 277 303 unlike burke and han s methods our algorithm does not introduce additional bound constraints the algorithm solves the same subproblems as the han powell sqp algorithm at feasible points of the original problem under certain assumptions it is shown that the algorithm coincides with the han powell method when the iterates are sufficiently close to the solution some global convergence results are proved and locally superlinear convergence results are also obtained preliminary numerical results are reported

p ranks and automorphism groups of algebraic curves let x be an irreducible complete nonsingular curve of genus g over an algebraically closed field k of positive characteristic p if 9 2 the automorphism group aut x of x is known to be a finite group and moreover its order is bounded from above by a polynomial in g of degree four stichtenoth in this paper we consider the frank zy of x and investigate relations between zy and aut x we show that zy affects the order of a sylow psubgroup of aut x 3 and that an inequality iaut x 84 9 1 9 holds for an ordinary i e zy g curve x 4

second order necessary and sufficient conditions for convex composite ndo in convex composite ndo one studies the problem of minimizing functions of the formf h f whereh m is a finite valued convex function andf n m is continuously differentiable this problem model has a wide range of application in mathematical programming since many important problem classes can be cast within its framework e g convex inclusions minimax problems and penalty methods for constrained optimization in the present work we extend the second order theory developed by a d ioffe in 11 12 13 for the case in whichh is sublinear to arbitrary finite valued convex functionsh moreover a discussion of the second order regularity conditions is given that illuminates their essentially geometric nature