system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

semigroup structural form for bernstein type operators and its applications in this note we provide a semigroup viewpoint for bernstein type operators a main ingredient of our approach is to obtain some explicit semigroup representation formulae which as simple forms are proposed for the fist time as direct applications we improve the corresponding results of de la cal and luquin 1992 1994 moreover some kinds of voronovskaja type results are made by using general semigroup expansion in the end we discuss corresponding generalizations of integral operators with some examples of hybrid durrmeyer type operators

frame expansions in separable banach spaces abstract banach frames are defined by straightforward generalization of hilbert space frames we characterize banach frames and x d frames in separable banach spaces and relate them to series expansions in banach spaces in particular our results show that we can not expect banach frames to share all the nice properties of frames in hilbert spaces

locally convex spaces containing no copy of c0 abstract we show that locally cinvex spaces which contain no copy of c 0 have a series of very nice properties

on converse approximation theorems abstract we establish sufficient conditions for obtaining a strong converse inequality of type b in terms of a unified k functional for a sequence of linear positive operators l n n 1 l n c 0 c 0 this k functional introduced by guo et al see e g s guo q qi strong converse inequalities for baskakov operators j approx theory 124 2003 219 231 will be considered for more general weight functions as applications we investigate the situation for baskakov type operators and szasz mirakjan type operators

batalin vilkovisky formalism in the functional approach to classical field theory we develop the batalin vilkovisky formalism for classical field theory on generic globally hyperbolic spacetimes a crucial aspect of our treatment is the incorporation of the principle of local covariance which amounts to formulate the theory without reference to a distinguished spacetime in particular this allows a homological construction of the poisson algebra of observables in classical gravity our methods heavily rely on the differential geometry of configuration spaces of classical fields

the microlocal spectrum condition and wick polynomials of free fields on curved spacetimes quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis we discuss a condition on the wave front set for the correspondingn point distributions called microlocal spectrum condition sc on minkowski space this condition is satisfied as a consequence of the usual spectrum condition based on radzikowski s determination of the wave front set of the two point function of a free scalar field satisfying the hadamard condition in the kay and wald sense we construct in the second part of this paper all wick polynomials including the energy momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition

approximation by modified srivastava gupta operators in the present paper we give a modified form of srivastava gupta operators which preserve the constant as well as linear functions we represent these operators as a special cases in terms of hypergeometric series we study some of the approximation properties and statistical approximation for these operators

some approximation properties of baskakov durrmeyer stancu operators abstract in this paper we are dealing with a new type of baskakov durrmeyer stancu bds operators d n f x defined by 1 4 first we estimate moments of these operators and also obtain the recurrence relations for the moments we estimate some approximation properties and asymptotic formulae for these operators in the last section we give better error estimations for the operators 1 4 using king type approach

faster rate of convergence on srivastava gupta operators abstract in this paper we consider a modification of srivastava gupta operators which is a general sequence of summation integral operators we are able to achieve faster convergence for our modified operators over the well known srivastava gupta operators our results include some approximation properties which include rate of convergence and voronovskaya kind results in the last section of this paper we give stancu variant of these operators

sensitivity analysis for variational inequalities in this paper we study the behavior of the local solutions of perturbed variational inequalities governed by perturbations to both the variational inequality function and the feasible region assuming appropriate second order and regularity conditions we show that the perturbed local solution set is lipschitz continuous and directionally differentiable even when the directional differentiability is not guaranteed we are still able to describe and characterize first order information concerning the perturbed local solution set we also discuss relations to nonlinear programming sensitivity analysis

approximation of unbounded functions by a new sequence of linear positive operators in the present paper we introduce a new sequence of linear positive operators to study the simultaneous approximation of unbounded functions

ricci flow from the renormalization of nonlinear sigma models in the framework of euclidean algebraic quantum field theory the perturbative approach to nonlinear sigma models and the associated renormalization group flow are discussed within the framework of euclidean algebraic quantum field theory and of the principle of general local covariance in particular we show in an euclidean setting how to define wick ordered powers of the underlying quantum fields and we classify the freedom in such procedure by extending to this setting a recent construction of khavkine melati and moretti for vector valued free fields as a by product of such classification we provide a mathematically rigorous proof that at first order in perturbation theory the renormalization group flow of the nonlinear sigma model is the ricci flow

combinations of integral operators in the present article we introduce a general sequence of summation integral operators the special cases of which are the well known phillips and the szasz beta operators here we consider the linear combinations of szasz beta operators and establish a voronovskaja type theorem and a direct result in terms of higher order modulus of continuity

banach spaces related to integrable group representations and their atomic decompositions i abstract we present a general theory of banach spaces which are invariant under the action of an integrable group representation and give their atomic decompositions with respect to coherent states i e the atoms arise from a single element under the group action several well known decomposition theories are contained as special examples and are unified under the aspect of group theory

the generally covariant locality principle a new paradigm for local quantum field theory a new approach to the model independent description of quantum field theories will be introduced in the present work the main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity thus giving rise to the concept of a locally covariant quantum field theory such locally covariant quantum field theories will be described mathematically in terms of covariant functors between the categories on one side of globally hyperbolic spacetimes with isometric embeddings as morphisms and on the other side of algebras with unital injective monomorphisms as morphisms moreover locally covariant quantum fields can be described in this framework as natural transformations between certain functors the usual haag kastler framework of nets of operator algebras over a fixed spacetime background manifold together with covariant automorphic actions of the isometry group of the background spacetime can be re gained from this new approach as a special case examples of this new approach are also outlined in case that a locally covariant quantum field theory obeys the time slice axiom one can naturally associate to it certain automorphic actions called relative cauchy evolutions which describe the dynamical reaction of the quantum field theory to a local change of spacetime background metrics the functional derivative of a relative cauchy evolution with respect to the spacetime metric is found to be a divergence free quantity which has as will be demonstrated in an example the significance of an energy momentum tensor up to addition of scalar functions for the locally covariant quantum field theory furthermore we discuss the functorial properties of state spaces of locally covariant quantum field theories that entail the validity of the principle of local definiteness

shrinking and boundedly complete schauder frames in frechet spaces abstract we study schauder frames in frechet spaces and their duals as well as perturbation results we define shrinking and boundedly complete schauder frames on a locally convex space study the duality of these two concepts and their relation with the reflexivity of the space we characterize when an unconditional schauder frame is shrinking or boundedly complete in terms of properties of the space several examples of concrete schauder frames in function spaces are also presented

approximation by stancu chlodowsky polynomials in this paper we investigate convergence and approximation properties of a chlodowsky type generalization of stancu polynomials we called stancu chlodowsky polynomials the rates of convergence of this generalization are obtained by means of modulus of continuity and by using the k functional of peetre we also present and prove theorems on weighted approximation and the order of approximation of continuous functions by these operators on all positive semi axis

linear yang mills theory as a homotopy aqft it is observed that the shifted poisson structure antibracket on the solution complex of klein gordon and linear yang mills theory on globally hyperbolic lorentzian manifolds admits retarded advanced trivializations analogs of retarded advanced green s operators quantization of the associated unshifted poisson structure determines a unique up to equivalence homotopy algebraic quantum field theory aqft i e a functor that assigns differential graded algebras of observables and fulfills homotopical analogs of the aqft axioms for klein gordon theory the construction is equivalent to the standard one while for linear yang mills it is richer and reproduces the brst bv field content gauge fields ghosts and antifields

the effective theory of strings we show that the nambu goto string and its higher dimensional generalizations can be quantized in the sense of an effective theory in any dimension of the target space the crucial point is to consider expansions around classical string configurations we are using tools from perturbative algebraic quantum field theory quantum field theory on curved spacetimes and the batalin vilkovisky formalism our model has some similarities with the luscher weisz string but we allow for arbitrary classical background string configurations and keep the diffeomorphism invariance

rate of approximation by a new sequence of linear positive operators abstract in the present paper we study the rate of pointwise approximation by a new sequence of linear positive operators for functions of bounded variation to prove the main result we have used some results of probability theory in the end we also introduce the bezier variant of these newly introduced sequences of linear positive operators

on the durrmeyer type modification of the q baskakov type operators abstract this paper deals with durrmeyer type generalization of q baskakov type operators using the concept of q integral which introduces a new sequence of positive q integral operators we show that this sequence is an approximation process in the polynomial weighted space of continuous functions defined on the interval 0 an estimate for the rate of convergence and weighted approximation properties are also obtained

szasz durrmeyer type operators based on charlier polynomials in the present paper we introduce a durrmeyer type modification of szasz operators based on charlier polynomials and study a voronovskaja type asymptotic theorem local approximation theorem weighted approximation statistical convergence and approximation of functions with derivatives of bounded variation for these operators

convergence of derivatives for certain mixed szasz beta operators in this paper we study the mixed summation integral type operators having szasz and beta basis functions in summation and integration respectively we obtain the rate of point wise convergence a voronovskaja type asymptotic formula and an error estimate in simultaneous approximation

partially b regular optimization and equilibrium problems this paper introduces a concept termed partial b regularity for a feasible solution to a bivariate constraint system and shows that this condition leads to the equivalence between the b stationarity of a pair of lifted and unlifted programs in particular for an optimization problem with a univariate pseudoconvex objective function constrained by such a nonconvex bivariate system partial b regularity provides a sufficient condition for a b stationary point to be globally optimal applications of partial b regularity to several classes of optimization and equilibrium problems are presented these include a lexicographic optimization problem a nonconvex mathematical program with equilibrium constraints mpec that arises from a convex implicit value function optimization problem and a nash equilibrium program with equilibrium constraints

algebraic structure of classical field theory i kinematics and linearized dynamics for real scalar fields we describe the elements of a novel structural approach to classical field theory inspired by recent developments in perturbative algebraic quantum field theory this approach is local and focuses mainly on the observables over field configurations given by certain spaces of functionals which are studied here in depth the analysis of such functionals is characterized by a combination of geometric analytic and algebraic elements which 1 make our approach closer to quantum field theory 2 allow for a rigorous analytic refinement of many computational formulae from the functional formulation of classical field theory and 3 provide a new pathway towards understanding dynamics particular attention will be paid to aspects related to nonlinear hyperbolic partial differential equations and their linearizations

direct limits of infinite dimensional lie groups compared to direct limits in related categories let g be a lie group which is the union of an ascending sequence g1 g2 of lie groups all of which may be infinite dimensional we study the question when g limgn in the category of lie groups topological groups smooth manifolds respectively topological spaces full answers are obtained for g the group diffc m of compactly supported c diffeomorphisms of a compact smooth manifold m and for test function groups cc m h of compactly supported smooth maps with values in a finite dimensional lie group h we also discuss the cases where g is a direct limit of unit groups of banach algebras a lie group of germs of lie group valued analytic maps or a weak direct product of lie groups

rate of convergence for certain families of summation integral type operators in this paper we study the rate of convergence for the iterative combinations of a certain family of linear positive operators in terms of higher order integral modulus of smoothness we have used the technique of linear approximating method namely steklov mean to prove the main result in the end we propose some other sequences of linear positive operators and obtain the recurrence formulae for the central moments voronovskaja type asymptotic formulae and error estimations

on the equivalence between complementarity systems projected systems and differential inclusions in this note we prove the equivalence under appropriate conditions between several dynamical formalisms projected dynamical systems two types of differential inclusions and a class of complementarity dynamical systems each of these dynamical systems can also be considered as a hybrid dynamical system this work both generalizes previous results and sheds some new light on the relationship between known formalisms besides it exclusively uses tools from convex analysis

some results on modified szasz mirakjan operators abstract in this paper we study the mixed summation integral type operators having szasz and beta basis functions we extend the study of gupta and noor v gupta m a noor convergence of derivatives for certain mixed szasz beta operators j math anal appl 321 1 2006 1 9 and obtain some direct results in local approximation without and with iterative combinations in the last section are established direct global approximation theorems

extremum seeking control of state constrained nonlinear systems an extremum seeking control problem is posed for a class of nonlinear systems with unknown dynamical parameters whose states are subject to convex pointwise inequality constraints using a barrier function approach an adaptive method is proposed for generating setpoints online which converge to the feasible minimizer of a convex objective function containing the unknown dynamic parameters a tracking controller regulates system states to the generated setpoint via state feedback while maintaining feasibility of the state constraints a simulation example demonstrates application of the method

anomalies in time ordered products and applications to the bv brst formulation of quantum gauge theories we show that every graded derivation on the algebra of free quantum fields and their wick powers in curved spacetimes gives rise to a set of anomalous ward identities for time ordered products with an explicit formula for their classical limit we study these identities for the koszul tate and the full brst differential in the bv brst formulation of perturbatively interacting quantum gauge theories and clarify the relation to previous results in particular we show that the quantum brst differential the quantum antibracket and the higher order anomalies form an l infty algebra the defining relations of this algebra ensure that the gauge structure is well defined on cohomology classes of the quantum brst operator i e observables furthermore we show that one can determine contact terms such that also the interacting time ordered products of multiple interacting fields are well defined on cohomology classes an important technical improvement over previous treatments is the fact that all our relations hold off shell and are independent of the concrete form of the lagrangian including the case of open gauge algebras

convergence of the q analogue of szasz beta operators in the present paper we introduce the q analogue of the well known szasz beta operators 11 we also establish the approximation properties of these operators and estimate convergence results in the end we propose an open problem

local duality of nonlinear programs it is shown that the second order sufficient necessary optimality condition for the dual of a nonlinear program is equivalent to the inverse of the hessian of the lagrangian being positive definite semidefinite on the normal cone to the local primal constraint surface this compares with the hessian itself being positive definite semidefinite on the tangent cone on the local primal constraint surface for the corresponding second order condition for the primal problem we also show that primal second order sufficiency necessity and dual second order necessity sufficiency is essentially equivalent to the hessian of the lagrangian being positive definite this follows from the following interesting linear algebra result a necessary and sufficient condition for a nonsingular symmetric n times n matrix to be positive definite is that for some subspace of r n the matrix must be positive definite on the subspace and its inverse be positive semidefinite on the orthogonal complement of the subspace

switching relay and complementarity systems a tutorial on their well posedness and relationships this paper reviews the relationships between switching systems defined from a partition of the state space into convex cells and relay or complementarity dynamical systems which are other classes of discontinuous systems well posedness results i e results on the existence and the uniqueness of solutions for different classes of relay and complementarity systems which are also switching systems are presented the reverse issue when can a switching system be rewritten equivalently as a relay or a complementarity system is also tackled many examples from mechanics circuits and biology illustrate the developments throughout the paper the paper focuses on systems with continuous solutions i e with no state jumps convexity is the central property

fully probabilistic design of hierarchical bayesian models the minimum cross entropy principle is an established technique for design of an unknown distribution processing linear functional constraints on the distribution more generally fully probabilistic design fpd chooses the distribution within the knowledge constrained set of possible distributions for which the kullback leibler divergence to the designer s ideal distribution is minimized these principles treat the unknown distribution deterministically in this paper fully probabilistic design is applied to hierarchical bayesian models for the first time yielding optimal design of a possibly nonparametric stochastic model for the unknown distribution this equips minimum cross entropy and fpd distributional estimates with measures of uncertainty it enables robust choice of the optimal model as well as randomization of this choice the ability to process non linear functional constraints in the constructed distribution significantly extends the applicability of these principles currently available fpd procedures for a merging of external knowledge b approximate learning and stabilized forgetting c decision strategy design and d local adaptive control design are unified for the first time via the hierarchical fpd framework of this paper

first order optimality conditions for degenerate index sets in generalized semi infinite optimization we present a general framework for the derivation of first order optimality conditions in generalized semi infinite programming since in our approach no constraint qualifications are assumed for the index set we can generalize necessary conditions given by ra ckmann and shapiro 1999 as well as the characterizations of local minimizers of order one which were derived by stein and still 2000 moreover we obtain a short proof for theorem 1 1 in jongen et al 1998 for the special case when the so called lower level problem is convex we show how the general optimality conditions can be strengthened thereby giving a generalization of theorem 4 2 in ra ckmann and stein 2001 finally if the directional derivative of a certain optimal value function exists and is subadditive with respect to the direction we propose a mangasarian fromovitz type constraint qualification and show that it implies an abadie type constraint qualification

on uniqueness of kuhn tucker multipliers in nonlinear programming recently fujiwara han and mangasarian introduced a new constraint qualification which is a slight tightening of the well known mangasarian fromovitz constraint qualification we show that this new qualification is a necessary and sufficient condition for the uniqueness of kuhn tucker multipliers we also show that it implies the satisfaction of second order necessary optimality conditions at a local minimum

stochastic multiobjective problems with complementarity constraints and applications in healthcare management abstract we consider a class of stochastic multiobjective problems with complementarity constraints smopccs in this paper we derive the first order optimality conditions including the clarke mordukhovich strong type stationarity in the pareto sense for the smopcc since these first order optimality systems involve some unknown index sets we reformulate them as nonlinear equations with simple constraints then we introduce an asymptotic method to solve these constrained equations furthermore we apply this methodology results to a patient allocation problem in healthcare management

the master ward identity and generalized schwinger dyson equation in classical field theory in the framework of perturbative quantum field theory a new universal renormalization condition called master ward identity was recently proposed by one of us m d in a joint paper with f m boas the main aim of the present paper is to get a better understanding of the master ward identity by analyzing its meaning in classical field theory it turns out that it is the most general identity for classical local fields which follows from the field equations it is equivalent to a generalization of the schwinger dyson equation and is closely related to the quantum action principle of lowenstein and lam as a byproduct we give a self contained treatment of peierls manifestly covariant definition of the poisson bracket

approximation for genuine summation integral type link operators in the present article we extend the studies on recently introduced sequence of the genuine summation integral type operators 7 here we establish a link between the genuine operators and the discrete operators we also establish a quantitative asymptotic formula a direct estimate in terms of ditzian totik modulus of smoothness and finally we present the rate of convergence for functions having derivatives of bounded variation

functional properties of hormander s space of distributions having a specified wavefront set the space mathcal d gamma prime of distributions having their wavefront sets in a closed cone gamma has become important in physics because of its role in the formulation of quantum field theory in curved spacetime in this paper the topological and bornological properties of mathcal d gamma prime and its dual mathcal e lambda prime are investigated it is found that mathcal d gamma prime is a nuclear semi reflexive and semi montel complete normal space of distributions its strong dual mathcal e lambda prime is a nuclear barrelled and ultra bornological normal space of distributions which however is not even sequentially complete concrete rules are given to determine whether a distribution belongs to mathcal d gamma prime whether a sequence converges in mathcal d gamma prime and whether a set of distributions is bounded in mathcal d gamma prime

direct result on exponential type operators in this paper we obtain a direct result and voronovskaya type asymptotic formula for the exponential type operators in simultaneous approximation with polynomial growth in the end we obtain the recurrence formulae for the central moments direct results and voronovskaya type asymptotic formulae for the various mixed summation integral type operators

global analysis of piecewise linear systems using impact maps and surface lyapunov functions this paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems pls this methodology infers global properties of pls solely by studying the behavior at switching surfaces associated with pls the main idea is to analyze impact maps i e maps from one switching surface to the next switching surface such maps are known to be unfriendly maps in the sense that they are highly nonlinear multivalued and not continuous we found however that an impact map induced by an linear time invariant flow between two switching surfaces can be represented as a linear transformation analytically parametrized by a scalar function of the state this representation of impact maps allows the search for surface lyapunov functions sulf to be done by simply solving a semidefinite program allowing global asymptotic stability robustness and performance of limit cycles and equilibrium points of pls to be efficiently checked this new analysis methodology has been applied to relay feedback on off and saturation systems where it has shown to be very successful in globally analyzing a large number of examples in fact it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology examples analyzed include systems of relative degree larger than one and of high dimension for which no other analysis methodology could be applied this success in globally analyzing certain classes of pls has shown the power of this new methodology and suggests its potential toward the analysis of larger and more complex pls

on approximation by a class of new bernstein type operators abstract this paper is concerned with a new type of the classical bernstein operators where the function is evaluated at intervals 0 1 1 n 1 we also make extensive study simultaneous approximation by the linear combination l n f k x of these new bernstein type operators l n f at the end of this paper we have given an other modification of these operators

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

solution differentiability for variational inequalities in this paper we study solution differentiability properties for variational inequalities we characterize frechet differentiability of perturbed solutions to parametric variational inequality problems defined on polyhedral sets our result extends the recent result of pang and it directly specializes to nonlinear complementarity problems variational inequality problems defined on perturbed sets and to nonlinear programming problems

lie group structures on quotient groups and universal complexifications for infinite dimensional lie groups we characterize the existence of lie group structures on quotient groups and the existence of universal complexifications for the class of baker campbell hausdorff bch lie groups which subsumes all banach lie groups and linear direct limit lie groups as well as the mapping groups ckr m g cr m g m k 1 for every bch lie group g second countable finite dimensional smooth manifold m compact subset k of m and 0 r also the corresponding test function groups dr m g kckr m g are bch lie groups

strong metric subregularity of mappings in variational analysis and optimization abstract although the property of strong metric subregularity of set valued mappings has been present in the literature under various names and with various equivalent definitions for more than two decades it has attracted much less attention than its older siblings the metric regularity and the strong metric regularity the purpose of this paper is to show that the strong metric subregularity shares the main features of these two most popular regularity properties and is not less instrumental in applications we show that the strong metric subregularity of a mapping f acting between metric spaces is stable under perturbations of the form f f where f is a function with a small calmness constant this result is parallel to the lyusternik graves theorem for metric regularity and to the robinson theorem for strong regularity where the perturbations are represented by a function f with a small lipschitz constant then we study perturbation stability of the same kind for mappings acting between banach spaces where f is not necessarily differentiable but admits a set valued derivative like approximation strong metric q subregularity is also considered where q is a positive real constant appearing as exponent in the definition rockafellar s criterion for strong metric subregularity involving injectivity of the graphical derivative is extended to mappings acting in infinite dimensional spaces a sufficient condition for strong metric subregularity is established in terms of surjectivity of the frechet coderivative and it is shown by a counterexample that surjectivity of the limiting coderivative is not a sufficient condition for this property in general then various versions of newton s method for solving generalized equations are considered including inexact and semismooth methods for which superlinear convergence is shown under strong metric subregularity as applications to optimization a characterization of the strong metric subregularity of the kkt mapping is obtained as well as a radius theorem for the optimality mapping of a nonlinear programming problem finally an error estimate is derived for a discrete approximation in optimal control under strong metric subregularity of the mapping involved in the pontryagin principle

on uniqueness of lagrange multipliers in optimization problems subject to cone constraints in this paper we study uniqueness of lagrange multipliers in optimization problems subject to cone constraints the main tool in our investigation of this question will be a calculus of dual polar cones we give sufficient and in some cases necessary conditions for uniqueness of lagrange multipliers in general banach spaces general results are then applied to two particular examples of the semidefinite and semi infinite programming problems respectively

stability analysis of variational inequalities and nonlinear complementarity problems via the mixed linear complementarity problem and degree theory this paper is concerned with the mixed linear complementarity problem and the role it and its variants play in the stability analysis of the nonlinear complementarity problem and the karush kuhn tucker system of a variational inequality problem under a nonsingular assumption the mixed linear complementarity problem can be converted to the standard problem in this case the rich theory of the latter can be directly applied to the former in this work we employ degree theory to derive some sufficient conditions for the existence of a solution to the mixed linear complementarity problem in the absence of the nonsingularity property next we extend this existence theory to the mixed nonlinear complementarity problem and establish a main stability result under a certain degree theoretic assumption concerning the linearized problem we then specialize this stability result and its consequences to the parametric variational inequality problem under the assumption of a unique set of multipliers finally we

karush kuhn tucker systems regularity conditions error bounds and a class of newton type methods we consider optimality systems of karush kuhn tucker kkt type which arise for example as primal dual conditions characterizing solutions of optimization problems or variational inequalities in particular we discuss error bounds and newton type methods for such systems an exhaustive comparison of various regularity conditions which arise in this context is given we obtain a new error bound under an assumption which we show to be strictly weaker than assumptions previously used for kkt systems such as quasi regularity or semistability equivalently the r0 property error bounds are useful among oth er things for identifying active constraints and developing efficient local algorithms we propose a family of local newton type algorithms this family contains some known active set newton methods as well as some new methods regularity conditions required for local superlinear convergence compare favorably with convergence conditions of nonsmooth newton methods and sequential quadratic programming methods

on constrained steady state regulation dynamic kkt controllers this technical note presents a solution to the problem of regulating a general nonlinear dynamical system to an economically optimal operating point the system is characterized by a set of exogenous inputs as an abstraction of time varying loads and disturbances the economically optimal operating point is implicitly defined as a solution to a given constrained convex optimization problem which is related to steady state operation the system outputs and the exogenous inputs represent respectively the decision variables and the parameters in the optimization problem the proposed solution is based on a specific dynamic extension of the karush kuhn tucker optimality conditions for the steady state related optimization problem which is conceptually related to the continuous time arrow hurwicz uzawa algorithm furthermore it can be interpreted as a generalization of the standard output regulation problem with respect to a constant reference signal

sensitivity analysis for nonlinear programs and variational inequalities with nonunique multipliers we extend the principal sensitivity analysis results for parametric nonlinear programs and variational inequalities by considering problems with nonunique optimal lagrange multipliers specifically we derive sufficient conditions for the existence continuity and directional differentiability of a locally unique perturbed solution of a nonlinear program or a variational inequality

complementarity modeling of hybrid systems a complementarity framework is described for the modeling of certain classes of mixed continuous discrete dynamical systems the use of such a framework is well known for mechanical systems with inequality constraints but we give a more general formulation which also applies for instance to switching control systems the main theoretical results in the paper are concerned with uniqueness of smooth continuations the solution of this problem requires the construction of a map from the continuous state to the discrete state a crucial technical tool is the so called linear complementarity problem from mathematical programming and we introduce various generalizations of this problem

on the accurate identification of active constraints we consider nonlinear programs with inequality constraints and we focus on the problem of identifying those constraints which will be active at an isolated local solution the correct identification of active constraints is important from both a theoretical and a practical point of view such an identification removes the combinatorial aspect of the problem and locally reduces the inequality constrained minimization problem to an equality constrained problem which can be more easily dealt with we present a new technique which identifies active constraints in a neighborhood of a solution and which requires neither complementary slackness nor uniqueness of the multipliers we also present extensions to variational inequalities and numerical examples illustrating the identification technique

stabilized sqp revisited the stabilized version of the sequential quadratic programming algorithm ssqp had been developed in order to achieve superlinear convergence in situations when the lagrange multipliers associated to a solution are not unique within the framework of fischer math program 94 91 124 2002 the key to local superlinear convergence of ssqp are the following two properties upper lipschitzian behavior of solutions of the karush kuhn tucker kkt system under canonical perturbations and local solvability of ssqp subproblems with the associated primal dual step being of the order of the distance from the current iterate to the solution set of the unperturbed kkt system according to fernandez and solodov math program 125 47 73 2010 both of these properties are ensured by the second order sufficient optimality condition sosc without any constraint qualification assumptions in this paper we state precise relationships between the upper lipschitzian property of solutions of kkt systems error bounds for kkt systems the notion of critical lagrange multipliers a subclass of multipliers that violate sosc in a very special way the second order necessary condition for optimality and solvability of ssqp subproblems moreover for the problem with equality constraints only we prove superlinear convergence of ssqp under the assumption that the dual starting point is close to a noncritical multiplier since noncritical multipliers include all those satisfying sosc but are not limited to them we believe this gives the first superlinear convergence result for any newtonian method for constrained optimization under assumptions that do not include any constraint qualifications and are weaker than sosc in the general case when inequality constraints are present we show that such a relaxation of assumptions is not possible we also consider applying ssqp to the problem where inequality constraints are reformulated into equalities using slack variables and discuss the assumptions needed for convergence in this approach we conclude with consequences for local regularization methods proposed in izmailov and solodov siam j optim 16 210 228 2004 wright siam j optim 15 673 676 2005 in particular we show that these methods are still locally superlinearly convergent under the noncritical multiplier assumption weaker than sosc employed originally

approximation by b spline convolution operators a probabilistic approach this paper is concerned with the approximation properties of convolution operators with respect to univariate b splines for such operators we give rates of uniform convergence in terms of the usual second modulus of smoothness at a length which depends on the distances between the knots and their multiplicity a reasonable balance between the degree of accuracy in the approximation and the degree of differentiability of the approximants is achieved by considering steklov operators built up from b splines with equidistant simple knots for which strong converse inequalities are given applications to simultaneous approximation and divided difference expansions and to estimate the infinite time ruin probabilities in a context of risk theory are also provided we use a probabilistic approach in the spirit of karlin et al j multivariate anal 20 1986 69 and ignatov and kaishev serdica 15 1989 91 based on the representation of b splines as the probability densities of linear combinations of uniform order statistics

generalized semi infinite programming a tutorial this tutorial presents an introduction to generalized semi infinite programming gsip which in recent years became a vivid field of active research in mathematical programming a gsip problem is characterized by an infinite number of inequality constraints and the corresponding index set depends additionally on the decision variables there exist a wide range of applications which give rise to gsip models some of them are discussed in the present paper furthermore geometric and topological properties of the feasible set and in particular the difference to the standard semi infinite case are analyzed by using first order approximations of the feasible set corresponding constraint qualifications are developed then necessary and sufficient first and second order optimality conditions are presented where directional differentiability properties of the optimal value function of the so called lower level problem are used finally an overview of numerical methods is given

some remarks on brs transformations anomalies and the cohomology of the lie algebra of the group of gauge transformations we show that ghosts in gauge theories can be interpreted as maurer cartan forms in the infinite dimensional group of gauge transformations we examine the cohomology of the lie algebra of and identify the coboundary operator with the brs operator we describe the anomalous terms encountered in the renormalization of gauge theories triangle anomalies as elements of these cohomology groups

on shrinking and boundedly complete schauder frames of banach spaces this paper studies schauder frames in banach spaces a concept which is a natural generalization of frames in hilbert spaces and schauder bases in banach spaces the associated minimal and maximal spaces are introduced as are shrinking and boundedly complete schauder frames our main results extend the classical duality theorems on bases to the situation of schauder frames in particular we will generalize james results on shrinking and boundedly complete bases to frames secondly we will extend his characterization of the reflexivity of spaces with unconditional bases to spaces with unconditional frames

relating nets and factorization algebras of observables free field theories in this paper we relate two mathematical frameworks that make perturbative quantum field theory rigorous perturbative algebraic quantum field theory paqft and the factorization algebras framework developed by costello and gwilliam to make the comparison as explicit as possible we use the free scalar field as our running example while giving proofs that apply to any field theory whose equations of motion are green hyperbolic which includes for instance free fermions the main claim is that for such free theories there is a natural transformation intertwining the two constructions in fact both approaches encode equivalent information if one assumes the time slice axiom the key technical ingredient is to use time ordered products as an intermediate step between a net of associative algebras and a factorization algebra

coefficient quantization for frames in banach spaces let ei be a fundamental system of a banach space we consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients we will concentrate on systems which are possibly redundant our model for this situation will be frames in banach spaces

on the iterates of a class of summation type linear positive operators this note is focused upon positive linear operators which preserve the quadratic test function by using contraction principle we study the convergence of their iterates

the microlocal spectrum condition initial value formulations and background independence we analyze implications of the microlocal spectrum hadamard condition for states in a linear quantum field theory on a globally hyperbolic spacetime m in the context of a distributional initial value formulation more specifically we work in 3 1 split m and give a bound independent of the spacetime metric on the wave front sets of the initial data for a quasi free hadamard state in a quantum field theory defined by a normally hyperbolic differential operator p acting in a vector bundle e m this aims at a possible way to apply the concept of hadamard states within approaches to quantum field theory gravity relying on a hamiltonian formulation potentially without a classical background metric g

the broken link between normality and regularity in the calculus of variations abstract there is a link between two well known constraint qualifications in nonlinear programming namely normality implying a positive cost multiplier and regularity the tangent cone and the set of tangential constraints coincide the former implies the latter this fact has been crucial and a cornerstone for establishing second order conditions in terms of tangential constraints for problems in the calculus of variations involving equality and inequality constraints one can derive second order conditions in terms of the tangent cone and state a conjecture based on tangential constraints which is the counterpart of that in nonlinear programming however as we show in this paper the link mentioned above between normality and regularity in the infinite dimensional case may fail to hold