oriented quantum algebras and invariants of knots and links abstract in our previous work oriented quantum algebras were motivated and introduced in a very natural categorical setting within the context of knots and links some examples were discussed and a rudimentary theory of oriented quantum algebras was sketched invariants of knots and links can be computed from oriented quantum algebras here we continue the study of oriented quantum algebras we view them from a more algebraic perspective and develop a more detailed theory for them and their associated invariants we study a class of examples associated with the homfly polynomial in depth

stability analysis of markovian jump stochastic bam neural networks with impulse control and mixed time delays this paper discusses the issue of stability analysis for a class of impulsive stochastic bidirectional associative memory neural networks with both markovian jump parameters and mixed time delays the jumping parameters are modeled as a continuous time discrete state markov chain based on a novel lyapunov krasovskii functional the generalized ito s formula mathematical induction and stochastic analysis theory a linear matrix inequality approach is developed to derive some novel sufficient conditions that guarantee the exponential stability in the mean square of the equilibrium point at the same time we also investigate the robustly exponential stability in the mean square of the corresponding system with unknown parameters it should be mentioned that our stability results are delay dependent which depend on not only the upper bounds of time delays but also their lower bounds moreover the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results consequently the results obtained in this paper are not only less conservative but also generalize and improve many earlier results finally two numerical examples and their simulations are provided to show the effectiveness of the theoretical results

a smoothing method for mathematical programs with equilibrium constraints the mathematical program with equilibrium constraints mpec is an optimization problem with variational inequality constraints mpec problems include bilevel programming problems as a particular case and have a wide range of applications mpec problems with strongly monotone variational inequalities are considered in this paper they are transformed into an equivalent one level nonsmooth optimization problem then a sequence of smooth regular problems that progressively approximate the nonsmooth problem and that can be solved by standard available software for constrained optimization is introduced it is shown that the solutions stationary points of the approximate problems converge to a solution stationary point of the original mpec problem numerical results showing viability of the approach are reported

elastoplastic truss design using a displacement based optimization abstract a displacement based optimization dbo method is applied to truss design problems with material nonlinearities to explore feasibility and verify efficiency of the method as compared to traditional structural optimization minimum weight truss sizing problems with various path independent elastoplastic laws including elastic perfectly plastic linear strain hardening and ramberg osgood models are investigated this type of material nonlinearity allows us to naturally extend the linear elastic truss sizing in the dbo setting to nonlinear problems to implement the methodology a computer program that uses the commercially available optimizer dot by vr d and imsl linear programming solver by visual numerics is developed several test problems are successfully solved using the dbo approach and solutions are compared to those available in the literature demonstrating significant reduction of computational time in comparison to the traditional structural optimization method in particular the dbo approach is found to be suitable for truss topology design since the method allows member areas to have cross sectional areas equal to zero exactly

newton type method for a class of mathematical programs with complementarity constraints in this paper we present a newton type method for a class of mathematical programs with complementarity constraints under the mpec licq we use the definition of b stationary point to construct a constrained equations model and apply the newton method to solve the problem at the end of this paper numerical results are reported to show our method s validity

solving the two dimensional constant quantum yang baxter equation a detailed analysis of the constant quantum yang baxter equation rk1k2j1j2 rl1k3k1j3rl2l3k2k3 rk2k3j2j3 rk1l3j1k3rl1l2k1k2 in two dimensions is presented leading to an exhaustive list of its solutions the set of 64 equations for 16 unknowns was first reduced by hand to several subcases which were then solved by computer using the grobner basis methods each solution was then transformed into a canonical form based on the various trace matrices of r for final elimination of duplicates and subcases if we use homogeneous parametrization the solutions can be combined into 23 distinct cases modulo the well known c p and t reflections and rotations and scalings r q q r q q 1

asymptotic stability in the pth moment for stochastic differential equations with levy noise abstract this paper is devoted to study a class of stochastic differential equations with levy noise in comparison to the standard gaussian noise levy noise is more versatile and interesting with a wider range of applications however levy noise makes the analysis more difficult owing to the discontinuity of its sample paths in this paper we attempt to overcome this difficulty we propose several sufficient conditions under which we investigate the long time behavior of the solution including the asymptotic stability in the pth moment and almost sure stability also we discuss two types of continuity of the solution continuous in probability and continuous in the pth moment finally we provide two examples to illustrate the effectiveness of the theoretical results

nonlinear robust optimization via sequential convex bilevel programming in this paper we present a novel sequential convex bilevel programming algorithm for the numerical solution of structured nonlinear min max problems which arise in the context of semi infinite programming here our main motivation are nonlinear inequality constrained robust optimization problems in the first part of the paper we propose a conservative approximation strategy for such nonlinear and non convex robust optimization problems under the assumption that an upper bound for the curvature of the inequality constraints with respect to the uncertainty is given we show how to formulate a lower level concave min max problem which approximates the robust counterpart in a conservative way this approximation turns out to be exact in some relevant special cases and can be proven to be less conservative than existing approximation techniques that are based on linearization with respect to the uncertainties in the second part of the paper we review existing theory on optimality conditions for nonlinear lower level concave min max problems which arise in the context of semi infinite programming regarding the optimality conditions for the concave lower level maximization problems as a constraint of the upper level minimization problem we end up with a structured mathematical program with complementarity constraints mpcc the special hierarchical structure of this mpcc can be exploited in a novel sequential convex bilevel programming algorithm we discuss the surprisingly strong global and locally quadratic convergence properties of this method which can in this form neither be obtained with existing sqp methods nor with interior point relaxation techniques for general mpccs finally we discuss the application fields and implementation details of the new method and demonstrate the performance with a numerical example

synchronization for time varying complex networks based on control in this paper the problem on synchronization is investigated for complex networks with time varying delay and without time varying delay by using control strategy together with some lyapunov krasovskii functions and effective mathematical techniques several conditions are derived to guarantee a class of complex networks with time varying and without time varying delays to be synchronized finally examples are given to illustrate the effectiveness of the proposed methods

competitive lotka volterra population dynamics with jumps abstract this paper considers competitive lotka volterra population dynamics with jumps the contributions of this paper are as follows a we show that a stochastic differential equation sde with jumps associated with the model has a unique global positive solution b we discuss the uniform boundedness of the p th moment with p 0 and reveal the sample lyapunov exponents c using a variation of constants formula for a class of sdes with jumps we provide an explicit solution for one dimensional competitive lotka volterra population dynamics with jumps and investigate the sample lyapunov exponent for each component and the extinction of our n dimensional model

space and time localization for the estimation of distributed parameters in a finite element model abstract in this paper we study the problem of estimating the possibly non homogeneous material coefficients inside a physical system from transient excitations and measurements made in a few points on the boundary we assume there is available an adequate finite element fem model of the system whose distributed physical parameters must be estimated from the experimental data we propose a space time localization approach that gives a better conditioned estimation problem without the need of an expensive regularization some experimental results obtained on an elastic system with random coefficients are given

real time updating of structural mechanics models using kalman filtering modified constitutive relation error and proper generalized decomposition the paper aims at proposing a new strategy for real time identification or updating of structural mechanics models defined as dynamical systems the main idea is to introduce the modified constitutive relation error concept which is a practical tool that enables to efficiently solve identification problems with highly corrupted data into the kalman filtering which is a classical framework for data assimilation furthermore a pgd based model reduction method is performed in order to optimize capabilities of the online updating strategy performances of the proposed approach in terms of robustness gain and computational cost reduction are illustrated on several unsteady thermal applications

inverse extraction of cohesive zone laws by field projection method using numerical auxiliary fields summary the cohesive zone law relates the cohesive tractions with the cohesive separations within the fracture process zone of a material and is used to quantify the strength and toughness of the material determining the material s cohesive zone law however is a nontrivial inverse problem of finding unknown tractions and separations from measurement data previously a field projection method was established to extract the cohesive zone laws from far field data using interaction j integrals between the physical field of interest and auxiliary analytical probing fields here we extend the universality of the field projection method and its ease of numerical implementation by using numerical auxiliary fields these numerical fields are generated by systematically imposing uniform surface tractions element by element along the crack faces in finite element models then interaction j and m integrals between these auxiliary probing fields and the measurement field are used to reconstruct the traction and separation relationship along the crack faces the effectiveness of this method in extracting the cohesive zone law from measured displacements in the far field region is demonstrated through numerical experiments copyright 2012 john wiley sons ltd

stability analysis for coupled systems with time delay on networks abstract in this paper the stability problem for some coupled systems with time delay on networks csdns is investigated we provide a systematic method for constructing a global lyapunov functional for csdns by using graph theory the stability uniform stability and global uniform stability of the systems are investigated and by using the lyapunov functional constructed some sufficient conditions of stability are obtained

a continuation method for strongly monotone variational inequalities we consider the variational inequality problem denoted by vip x f wheref is a strongly monotone function and the convex setx is described by some inequality and possibly equality constraints this problem is solved by a continuation or interior point method which solves a sequence of certain perturbed variational inequality problems these perturbed problems depend on a parameter 0 it is shown that the perturbed problems have a unique solution for all values of 0 and that any sequence generated by the continuation method converges to the unique solution of vip x f under a well known linear independence constraint qualification licq we also discuss the extension of the continuation method to monotone variational inequalities and present some numerical results obtained with a suitable implementation of this method 1998 the mathematical programming society inc published by elsevier science b v

concrete structure design using mixed integer nonlinear programming with complementarity constraints we present a mixed integer nonlinear programming minlp formulation to achieve minimum cost designs for reinforced concrete rc structures that satisfy building code requirements the objective function includes material and labor costs for concrete steel reinforcing bars and formwork according to typical contractor methods restrictions enforce correct geometry of the cross section dimensions for each element and relative sizes of cross section dimensions of elements within the structure other restrictions define a stiffness and displacement correlation among all structural elements via finite element analysis the design of minimum cost rc structures introduces a new class of optimization problems namely mixed integer nonlinear programs with complementarity constraints the complementarity constraints are used to model rc element strength and american concrete institute code required safety factors we reformulate the complementarity constraints as nonlinear equations and show that the resulting

convex two level optimization in this paper a model for a two level planning problem is presented in the form of a static stackelberg game by assumption play is sequential and noncooperative however the leader can influence the actions of the followers through a set of coordination variables while the followers responses may partly determine the leader s payoff under certain convexity assumptions it is shown that the feasible region induced by the leader is continuous in the original problem variables this observation coupled with two corollary results are used as a basis for a hybrid algorithm which clings to the inducible region until a local optimum is found a branching scheme is then employed to located other segments of the region eventually terminating with the global optimum a number of examples are given to highlight the results while the algorithm s performance is tested in a comparison with two other procedures

an fe mpec approach for limit load evaluation in the presence of contact and displacement constraints abstract this paper describes a mathematical programing based approach for the direct limit load evaluation of a structural system under simultaneous contact and limited displacement conditions the contact model we adopt can simulate either a classical unilateral nonassociative coulomb friction situation or a cohesive fracture idealization at the potential discontinuity interface between contacting bodies the discrete fe model is constructed using locking free mixed finite elements the main feature and novelty of our proposed approach is to compute in a single step the maximum load capacity of the structure such that both the imposed displacement limitations and the contact conditions are satisfied in essence the formulation is a nontrivial extension of classical limit analysis the analysis is cast in its most natural form namely in mixed static kinematic variables and leads to what is known in the mathematical programing literature as a mathematical program with equilibrium constraints or mpec a nonlinear programing nlp based algorithm is proposed to solve the mpec two examples are provided to illustrate application of the proposed scheme and some comments regarding the various advantages of the adopted mathematical programing framework are made

some feasibility issues in mathematical programs with equilibrium constraints this paper is concerned with some feasibility issues in mathematical programs with equilibrium constraints mpecs where additional joint constraints are present that must be satisfied by the state and design variables of the problems we introduce sufficient conditions that guarantee the feasibility of these mpecs it turns out that these conditions also guarantee the feasibility of the quadratic programming qp subproblems arising from the penalty interior point algorithm pipa and the sequential quadratic programming sqp algorithm for solving mpecs thus the same conditions ensure that these algorithms are applicable for solving this class of jointly constrained mpecs

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

mathematical programs with complementarity constraints convergence properties of a smoothing method in this paper optimization problems p with complementarity constraints are considered characterizations for local minimizers bar x of p of orders 1 and 2 are presented we analyze a parametric smoothing approach for solving these programs in which p is replaced by a perturbed problem p tau depending on a small parameter tau we are interested in the convergence behavior of the feasible set cal f tau and the convergence of the solutions bar x tau of p tau for tau to 0 in particular it is shown that under generic assumptions the solutions bar x tau are unique and converge to a solution bar x of p with a rate cal o sqrt tau moreover the convergence for the hausdorff distance d cal f tau cal f between the feasible sets of p tau and p is of order cal o sqrt tau

on the solution of a minimum weight elastoplastic problem involving displacement and complementarity constraints this paper deals with a special class of minimum weight design problem involving discretized structures holonomic reversible plasticity and constraints on displacements a key feature of the optimization problem is the presence of complementarity conditions involving the orthogonality of two sign constrained vectors this problem falls within the important class of so called mathematical programs with equilibrium constraints mpecs two simple algorithms are proposed to solve our synthesis problem and application is illustrated by some examples concerning truss like structures

some novel approaches on state estimation of delayed neural networks this paper studies the issue of state estimation for a class of neural networks nns with time varying delay a novel lyapunov krasovskii functional lkf is constructed where triple integral terms are used and a secondary delay partition approach sdpa is employed compared with the existing delay partition approaches the proposed approach can exploit more information on the time delay intervals by taking full advantage of a modified wirtinger s integral inequality mwii improved delay dependent stability criteria are derived which guarantee the existence of desired state estimator for delayed neural networks dnns a better estimator gain matrix is obtained in terms of the solution of linear matrix inequalities lmis in addition a new activation function dividing method is developed by bringing in some adjustable parameters three numerical examples with simulations are presented to demonstrate the effectiveness and merits of the proposed methods

graph theory based approach for stability analysis of stochastic coupled systems with levy noise on networks in this paper a novel class of stochastic coupled systems with levy noise on networks scslnns is presented both white noise and levy noise are considered in the networks by exploiting graph theory and lyapunov stability theory criteria ensuring p th moment exponential stability and stability in probability of these scslnns are established respectively these principles are closely related to the topology of the network and the perturbation intensity of white noise and levy noise moreover to verify the theoretical results stochastic coupled oscillators with levy noise on a network and stochastic volterra predator prey system with levy noise are performed finally a numerical example about oscillators network is provided to illustrate the feasibility of our analytical results

mean square exponential stability of stochastic nonlinear delay systems abstractin this paper we are concerned with the stability of stochastic nonlinear delay systems different from the previous literature we aim to show that when the determinate nonlinear delay system is globally exponentially stable the corresponding stochastic nonlinear delay system can be mean square globally exponentially stable in particular we remove the linear growth condition and introduce a new polynomial growth condition for g x t x t t which overcomes the limitation of application scope and the boundedness of diffusion term form finally we provide an example to illustrate our results

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

a neural network approach for solving nonlinear bilevel programming problem a neural network model is presented for solving nonlinear bilevel programming problem which is a np hard problem the proposed neural network is proved to be lyapunov stable and capable of generating approximal optimal solution to the nonlinear bilevel programming problem the asymptotic properties of the neural network are analyzed and the condition for asymptotic stability solution feasibility and solution optimality are derived the transient behavior of the neural network is simulated and the validity of the network is verified with numerical examples

stationary distribution for stochastic coupled systems with regime switching and feedback control abstract the existence of stationary distribution for stochastic coupled systems with regime switching and feedback control is investigated in terms of model feedback control is concerned in the existence of stationary distribution for stochastic coupled systems with regime switching in terms of method graph theory is employed to investigate the existence of stationary distribution for stochastic coupled systems with regime switching and some sufficient conditions are given based on lyapunov method connected with the graph theory and the m matrix method to ensure the existence of stationary distribution which reveals the influences that feedback control brings on stationary distribution and the existing area is related to stochastic disturbance feedback control and coupling strength furthermore the application to stochastic coupled oscillators with feedback control and regime switching can demonstrate the practicability of our theoretical results finally a numerical example is presented to verify the effectiveness and availability of our results as well as the superiority of influence that feedback control brings on stationary distribution

efficient computation of multiple solutions in quasibrittle fracture analysis we propose a novel and efficient computational scheme for capturing the multiplicity of solutions that may exist at any loading step of a quasibrittle fracture analysis formulated as a linear complementarity problem lcp the algorithm proposed is based on successively augmenting the current lcp by complementarity constraints that effectively remove previously found solutions from the solution set we focus on the single step or so called holonomic analysis for mode i behavior the performance of the proposed approach is illustrated by means of physically meaningful benchmark problems

stability analysis of markov switched stochastic differential equations with both stable and unstable subsystems abstract this paper discusses the asymptotic stability of markov switched stochastic differential equations by using the method of multiple lyapunov functions we provide sufficient conditions for stochastic asymptotic stability of markov switched stochastic differential equations with both stable and unstable subsystems via the inequality based on the multiple lyapunov functions and the stationary distribution of markovian switching process particularly our results include some existing results as special cases and improve some results in the literature two examples are given to illustrate the effectiveness of the obtained results

parameter identification of quasibrittle materials as a mathematical program with equilibrium constraints the identification of the cohesive fracture parameters of quasibrittle materials forms the focus of the present work this important and challenging task is formulated as an inverse problem requiring the solution of a special type of constrained optimization problem known as a mathematical program with equilibrium constraints mpec a key feature of which is the presence of complementarity conditions involving the orthogonality of two nonnegative vectors we propose a simple scheme based on transforming the mpec into a standard nonlinear programming problem through appropriate smoothing of the complementarity constraints for solving the parameter identification problem some computational results using actual experimentally obtained data are presented to assess the effectiveness of the approach

parameter identification of a cohesive crack model by kalman filter abstract the kalman filter kf methodology is apt to solve parameter identification inverse problems in a statistical context through a sequence of estimations which starts from an a priori estimation by an expert bayesian approach and exploits a time stepping flow of experimental data until convergence is empirically ascertained such methodology is here adopted for the identification of the material parameters together with their uncertainties in a mode i cohesive crack model on the basis of experimental data generated by wedge splitting tests on concrete specimens the simulation of the experiments is based on the assumptions of a piecewise linear cohesive model with four parameters to identify on the crack path and of linear elasticity elsewhere in view of regularly progressive fracture processes the discrete crack model and consequently the overall finite element analysis are formulated as linear complementarity problems this mathematical construct is exploited to obtain the sensitivity matrix key ingredient of the kf extended to nonlinear inverse problems in a computationally convenient closed form various issues peculiar of kf identification in the present mechanical context are critically discussed in the light of the numerical solutions achieved

mpcc critical point theory we study mathematical programs with complementarity constraints mpcc from a topological point of view special focus will be on c stationary points under the linear independence constraint qualification licq we derive an equivariant morse lemma at nondegenerate c stationary points then two basic theorems from morse theory deformation theorem and cell attachment theorem are proved outside the c stationary point set continuous deformation of lower level sets can be performed as a consequence the topological data such as the number of connected components then remain invariant however when passing a c stationary level the topology of the lower level set changes via the attachment of a q dimensional cell the dimension q equals the stationary c index of the nondegenerate c stationary point the stationary c index depends on both the restricted hessian of the lagrangian and the lagrange multipliers related to biactive complementarity constraints finally some relations with other stationarity concepts such as w a m s and b stationarity are discussed

a discrete formulation for elastic solids with damaging interfaces abstract an elastic solid with embedded interfaces loci of possible displacement discontinuities is considered here decohesion and quasi brittle fracture processes are simulated by making use of softening interface laws which relate tractions to displacements jumps a discrete formulation in terms of interface variables only is obtained the space discretization is carried out by means of a mixed finite element approach in which all interface variables are modelled study of uniqueness of the rate problem formulated in terms of interface variables and of stability of the equilibrium states is presented some examples are shown in order to clarify the formulation

global stability problem for coupled systems of differential equations on networks the global stability problem of equilibria is investigated for coupled systems of differential equations on networks using results from graph theory we develop a systematic approach that allows one to construct global lyapunov functions for large scale coupled systems from building blocks of individual vertex systems the approach is applied to several classes of coupled systems in engineering ecology and epidemiology and is shown to improve existing results

a cascade optimization methodology for automatic parameter identification and shape process optimization in metal forming simulation computer simulations of metal forming processes using the finite element method fem are today well established this form of simulation uses an increasing number of sophisticated geometrical and material models relying on a certain number of input data which are not always readily available the aim of inverse problems which will be considered here is to determine one or more of the input data relating to these forming process simulations thereby leading to a desired result in this paper we will focus on two categories of such inverse problems the first category consists of parameter identification inverse problems these involve evaluating the material parameters for material constitutive models that would lead to the most accurate results with respect to physical experiments i e minimizing the difference between experimental results and fem simulations the second category consists of shape process optimization inverse problems these involve determining the initial geometry of the specimen and or the shape of the forming tools as well as some parameters of the process itself in order to provide the desired final geometry after the forming process these two categories of inverse problems can be formulated as optimization problems in a similar way i e by using identical optimization algorithms in this paper we intend firstly to solve these two types of optimization problems by using different non linear gradient based optimization methods and secondly to compare their efficiency and robustness in a variety of numerical applications

active set algorithm for mathematical programs with linear complementarity constraints in the paper an incomplete active set algorithm is given for mathematical programs with linear complementarity constraints mplcc at each iteration a finite number of inner iterations are contained for approximately solving the relaxed nonlinear optimization problem if the feasible region of the mplcc is bounded under the uniform linear independence constraint qualification licq any cluster point of the sequence generated from the algorithm is a b stationary point of the mplcc preliminary numerical tests show that the algorithm is promising

exponential stability of stochastic complex networks with multi weights based on graph theory abstract in this paper a novel approach to exponential stability of stochastic complex networks with multi weights is investigated by means of the graph theoretical method new sufficient conditions are provided to ascertain the moment exponential stability and almost surely exponential stability of stochastic complex networks with multiple weights it is noted that our stability results are closely related with multi weights and the intensity of stochastic disturbance numerical simulations are also presented to substantiate the theoretical results

the explicit inverse of the stiffness matrix abstract in two recent papers the author has given the exact analytic expression of the internal forces in linear elastic structures composed of uniform prismatic elements it was shown that the member forces are the ratios of two multilinear homogeneous polynomials in the unimodal stiffnesses of the elements of the structure the order of the polynomials is equal to the number of nodal degrees of freedom of the structure the number of terms of each polynomial is equal to the number of statically determinate stable substructures which can be derived from the original structure the coefficients of the polynomials can be computed by employing the equilibrium equations and by enforcing global compatibility of deformations it was found empirically that the coefficients of the polynomial in the denominator were numerically equal to the square of the determinants of the statics matrices of the respective statically determinate substructures as a consequence the denominator became the sum of the stiffness matrices of the statically determinate substructures this is in fact the binet cauchy form of the determinant of the stiffness matrix of the structure bearing in mind that the inverse of the stiffness matrix can be expressed as the ratio of the adjoint matrix of the stiffness matrix divided by the determinant of the stiffness matrix it became clear that the expressions of the stress resultants stem from an explicit expression of the adjoint the explicit expression of the adjoint of the stiffness matrix lies at the heart of this paper it is shown that the adjoint is a congruent transformation of the n 1 compound of the stiffness matrix where n is the number of degrees of freedom of the structure this cleared the way to use the binct cauchy theorem on the product of compound matrices to obtain an explicit expression for the adjoint and ipso facto for the inverse of the stiffness matrix having now the displacements of the structure the expression of the stress resultants which was obtained independently emerges in a very elegant manner the member forces in a structure can be expressed as the weighted sum of the member forces in all its determinate substructures when subjected to the applied loads the weighting factors are the ratios of the determinants of he stiffness matrices of the substructures to the determinant of the stiffness matrix of the original structure both the explicit inverse of the stiffness matrix and the expression of the internal forces in the structure are at present of a theoretical nature the number of terms involved in the polynomials is simply excessive for common engineering structures however ongoing reseach may yield more applicable expressions to be used for instance in he field of automated design of structures the theory is illustrated with the explicit analysis of a stayed mast

on stability of the feasible set of a mathematical problem with complementarity problems the feasible set of mathematical programs with complementarity constraints mpcc is considered we discuss local stability of the feasible set with respect to perturbations up to first order of the defining functions here stability refers to homeomorphy invariance under small perturbations for stability we propose a kind of mangasarian fromovitz condition mfc and its stronger version smfc mfc is a natural constraint qualification for c stationarity and smfc is a generalization of the well known clarke s maximal rank condition it turns out that smfc implies local stability mfc and smfc coincide in the case where the number of complementarity constraints k equals the dimension of the state space n moreover the equivalence of mfc and smfc is also proven for the cases k 2 as well as under linear independence constraint qualification licq for mpcc

identification of cohesive crack fracture parameters by evolutionary search this paper is concerned with the application and performance of two evolutionary search techniques to identify the parameters characterizing mode i cohesive crack models in particular genetic based heuristic schemes implemented via a classical genetic algorithm and also as a differential evolution process are considered actual experimental data are used to assess the schemes for both piecewise linear and nonlinear softening models the results of these two adaptive algorithms are also compared with the performance of a previously proposed local optimization approach involving formulation of the inverse problem as a mathematical program with equilibrium constraints

synchronizing nonlinear complex networks via switching disconnected topology the current theoretical study on the synchronization mechanism of complex networks mainly focuses on fixed connected topology or switching balanced topology which is heavily based on constructing common smooth lyapunov functions however for complex networks with nonlinear node dynamics it is still unknown whether such kind of networks can synchronize under the condition of switching directed and disconnected topology by employing the ideas of sequential connectivity and joint connectivity this paper finds that complex networks with one sided lipschitz node dynamics can realize synchronization even if the network topology is not connected at any time instant by iteratively estimating the maximal distance between different nodes this paper gives several sufficient conditions on synchronization of nonlinear complex networks under switching disconnected topology finally simulation examples validate the main results

on two level optimization decentralized planning has long been recognized as an important decision making problem many approaches based on the concepts of large scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which have often existed in practice similarly tractable game theoretic approaches have not allowed for a continuous solution space in which one player s decision restricts the feasible choices of another this correspondence offers a formulation to help model this type of decision making hierarchy characterizations and algorithmic approaches for a class of two level problems are discussed

how to solve a semi infinite optimization problem abstract after an introduction to main ideas of semi infinite optimization this article surveys recent developments in theory and numerical methods for standard and generalized semi infinite optimization problems particular attention is paid to connections with mathematical programs with complementarity constraints lower level wolfe duality semi smooth approaches as well as branch and bound techniques in adaptive convexification procedures a section on recent genericity results includes a discussion of the symmetry effect in generalized semi infinite optimization

an approximate programming method based on the simplex method for bilevel programming problem many real problems can be modeled to the problems with a hierarchical structure and bilevel programming is a useful tool to solve the hierarchical optimization problems so the bilevel programming is widely applied and numerous methods have been proposed to solve this programming in this paper we propose an approximate programming algorithm to solve bilevel nonlinear programming problem finally the example illustrates the feasibility of the proposed algorithm

smooth sqp methods for mathematical programs with nonlinear complementarity constraints mathematical programs with nonlinear complementarity constraints are reformulated using better posed but nonsmooth constraints we introduce a class of functions parameterized by a real scalar to approximate these nonsmooth problems by smooth nonlinear programs this smoothing procedure has the extra benefits that it often improves the prospect of feasibility and stability of the constraints of the associated nonlinear programs and their quadratic approximations we present two globally convergent algorithms based on sequential quadratic programming sqp as applied in exact penalty methods for nonlinear programs global convergence of the implicit smooth sqp method depends on existence of a lower level nondegenerate strictly complementary limit point of the iteration sequence global convergence of the explicit smooth sqp method depends on a weaker property i e existence of a limit point at which a generalized constraint qualification holds we also discuss some practical matters relating to computer implementations

estimation of model parameters in nonlocal damage theories by inverse analysis techniques abstract the parameters identification problem of the gradient enhanced continuum damage model is examined by means of an inverse analysis different related issues are analyzed i the investigation of the limits of applicability and predictability of the adopted numerical model and ii the problem of objectively extracting material properties from a structural response a necessary condition for an adequate identification of the model parameters is the well posedness of the inverse problem the results show that this requirement is obtained only if additional averaged local experimental information is involved in the inverse procedure in addition to the global structural force deformation response moreover the adopted numerical model reveals limitations in predicting the entire size effect curve of tensile tests on dog bone shaped concrete specimens

parameter identification in explicit structural dynamics performance of the extended kalman filter abstract an extended kalman filter ekf approach is adopted in this paper for structural systems subject to dynamic loadings to simultaneously estimate the state and calibrate constitutive parameters to pursue this aim after space and time discretizations a joint system state vector is introduced gathering nodal displacements and constitutive parameters to be identified because of the linearization of the discretized equations governing filter updates the ekf can lead to inaccurate model calibration it is shown that even though the state of the system is always followed with a high level of accuracy unsatisfactory parameter estimations can be obtained in the case of degrading strength of the structure that is in the case of softening both single degree of freedom dof and multi dof dynamic systems are analyzed to detect the possible sources of this inaccuracy

new models for optimal truss topology in limit design based on unified elastic plastic analysis abstract this paper presents several equivalent formulations for a structural design problem where the load carrying capacity is maximized for a prescribed volume subject to bounds on complementary energy and stresses this limit design model covers the full range of strictly elastic elastic plastic and strictly plastic designs and is based on the unified analysis model of ben tal and taylor 1 while this design model is convex it is nonlinearly constrained and is of a very high dimension for topology design problems application of duality principles leads to several simpler but nonsmooth equivalent models in particular for the case when the design variables do not have explicit bounds the dual models reduce to a minimization subject to a single linear constraint of a pointwise maximum of a finite number of convex functions more importantly these simpler design models are of greatly reduced size since they contain only nodal variables further the two cases of strictly plastic as well as strictly elastic limit design models can be reduced to linear programs both of which unexpectedly are shown to be equivalent to the more widely studied model for minimum compliance topology design of elastic trusses several numerical examples illustrate the usefulness of these new dual formulations

mathematical programming approaches for the safety assessment of semirigid elastoplastic frames abstract this paper presents two complementary mathematical programming based approaches for the accurate safety assessment of semirigid elastoplastic frames under quasistatic loads the inelastic behavior of the flexible connections and material plasticity are accommodated through piecewise linearized nonlinear yield surfaces as is necessary for this class of structures geometric nonlinearity is taken into account moreover only a 2nd order geometric approximation is included as this is sufficiently accurate for practical structures the work described has a twofold contribution first we develop an algorithm that can robustly and efficiently process the complete path dependent nonholonomic response of the structure in a stepwise path independent holonomic fashion the governing formulation is cast in mixed static kinematic variables and leads naturally to what is known in the mathematical programming literature as a mixed complementarity problem mcp the novelty of the proposed algorithm is that it processes the mcp directly without using some iterative and often cumbersome predictor corrector procedure second in the spirit of simplified analyses the classical limit analysis approach is extended to compute the limit load multiplier under the simultaneous influence of joint flexibility material and geometric nonlinearities and limited ductility our formulation is an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints mpec various nonlinear programming based algorithms are proposed to solve the mpec finally four numerical examples concerning practical structures and benchmark cases are provided to illustrate application of the analyses as well as to validate the accuracy and robustness of the proposed schemes

razumikhin type theorem for stochastic functional differential equations with levy noise and markov switching abstractthis paper is devoted to study the well known razumikhin type theorem for a class of stochastic functional differential equations with levy noise and markov switching in comparison to the standard gaussian noise levy noise and markov switching make the analysis more difficult owing to the discontinuity of its sample paths in this paper we attempt to overcome this difficulty by using the razumikhin method and lyapunov functions we obtain several razumikhin type theorems to prove the pth moment exponential stability of the suggested system based on these results we further discuss the pth moment exponential stability of stochastic delay differential equations with levy noise and markov switching in particular the results obtained in this paper improve and generalise some previous works given in the literature finally an example is provided to illustrate the effectiveness of the theoretical results

robust assessment of collapse resistance of structures under uncertain loads based on info gap model abstract the paper proposes a pair of novel mathematical programming based approaches which directly determine the worst collapse load limit in one case and the best limit in the other case of rigid perfectly plastic structures subjected to uncertain but bounded applied loads using an info gap model the methods take advantage of the important properties in which the worst collapse load limit defined for an uncertain static formulation is equivalent to the most favourable solution of the uncertain kinematic limit analysis problem and vice versa for the best collapse load limit the formulation for capturing the worst collapse load limit robust worst case solution takes the form as a mathematical program with equilibrium constraints that is processed using a penalty algorithm whilst that for the best collapse load limit is a standard linear programming problem the efficiency and robustness of the proposed schemes are evidenced from a number of successfully solved examples

the existence of periodic solutions for discrete time coupled systems on networks with time varying delay abstract this paper deals with the existence of periodic solutions for discrete time coupled systems on networks with time varying delay dcsntd based on coincidence degree theory graph theory and lyapunov method a systematic method is given to study the existence of periodic solutions for dcsntd a lyapunov type theorem and a coefficient type criterion are derived respectively furthermore we apply this novel approach to research the existence of periodic solutions for discrete time coupled oscillators with time varying delay finally a numerical simulation is presented to illustrate the effectiveness and feasibility of our results

a numerical approach to optimization problems with variational inequality constraints optimization problems with variational inequality constraints are converted to constrained minimization of a local lipschitz function to this minimization a non differentiable optimization method is used the required subgradients of the objective are computed by means of a special adjoint equation besides tests with some academic examples the approach is applied to the computation of the stackelberg cournot nash equilibria and to the numerical solution of a class of quasi variational inequalities

stability analysis of stochastic delayed complex networks with multi weights based on razumikhin technique and graph theory abstract in this paper a novel kind of stochastic delayed complex networks with multi weights sdcnmw is considered we first split sdcnmw into multiple stochastic complex networks with single weight this paper is mainly concerned with the issues of exponential stability for sdcnmw a global lyapunov functional is constructed by a graph theoretical approach based on kirchhoff s matrix tree theorem razumikhin type theorem is presented by stochastic stability theory and razumikhin technique an easy verified coefficients type theorem is also given finally theoretical results are illustrated by stochastic oscillators network successfully

on bilevel programming part i general nonlinear cases this paper is concerned with general nonlinear nonconvex bilevel programming problems blpp we derive necessary and sufficient conditions at a local solution and investigate the stability and sensitivity analysis at a local solution in the blpp we then explore an approach in which a bundle method is used in the upper level problem with subgradient information from the lower level problem two algorithms are proposed to solve the general nonlinear blpp and are shown to converge to regular points of the blpp under appropriate conditions the theoretical analysis conducted in this paper seems to indicate that a sensitivity based approach is rather promising for solving general nonlinear blpp

nonholonomic elastoplastic analysis involving unilateral frictionless contact as a mixed complementarity problem this paper deals with the elastoplastic analysis of suitably discretized elastoplastic structures under frictionless unilateral contact conditions whilst the mathematical programming formulation we adopt can cater equally for hardening as well as softening path dependent nonholonomic plasticity the state problem involving softening is by far the more difficult to solve in view of the inherent nonconvex nature of the underlying mathematical program we propose a novel description of a fairly general class of piecewise linear softening laws and investigate use of an approximate stepwise holonomic path independent approach for capturing the evolution of the structure with softening and or hardening constitutive laws this finite step problem is formulated in a specific way to take advantage of the use of a robust and industry standard complementarity solver named path from within the gams modeling environment we illustrate its application on truss like structures

multiplier convergence in trust region methods with application to convergence of decomposition methods for mpecs we study piecewise decomposition methods for mathematical programs with equilibrium constraints mpecs for which all constraint functions are linear at each iteration of a decomposition method one step of a nonlinear programming scheme is applied to one piece of the mpec to obtain the next iterate our goal is to understand global convergence to b stationary points of these methods when the embedded nonlinear programming solver is a trust region scheme and the selection of pieces is determined using multipliers generated by solving the trust region subproblem to this end we study global convergence of a linear trust region scheme for linearly constrained nlps that we call a trust search method the trust search has two features that are critical to global convergence of decomposition methods for mpecs a robustness property with respect to switching pieces and a multiplier convergence result that appears to be quite new for trust region methods these combine to clarify and strengthen global convergence of decomposition methods without resorting either to additional conditions such as eventual inactivity of the trust region constraint or more complex methods that require a separate subproblem for multiplier estimation

global stability analysis for stochastic coupled systems on networks this paper considers the global stability problem for some stochastic coupled systems on networks scsns we provide a systematic method for constructing a global lyapunov function for these scsns by using graph theory and the lyapunov second method consequently a new global stability principle which has a close relation to the topology property of the network is given as an application to the results we employ the principle to two well known coupled systems in physical and ecology and then some easy verified sufficient conditions which guarantee the global stability are obtained

modeling and computing two settlement oligopolistic equilibrium in a congested electricity network a model of two settlement electricity markets is introduced which accounts for flow congestion demand uncertainty system contingencies and market power we formulate the subgame perfect nash equilibrium for this model as an equilibrium problem with equilibrium constraints epec in which each firm solves a mathematical program with equilibrium constraints mpec the model assumes linear demand functions quadratic generation cost functions and a lossless dc network resulting in equilibrium constraints as a parametric linear complementarity problem lcp we introduce an iterative procedure for solving this epec through repeated application of an mpec algorithm this mpec algorithm is based on solving quadratic programming subproblems and on parametric lcp pivoting numerical examples demonstrate the effectiveness of the mpec and epec algorithms and the tractability of the model for realistic size power systems

fitting data with errors in all variables using the huber m estimator this article is concerned with the problem of data fitting where the model is nonlinear in the free parameters using the huber m estimator under the assumption that there are significant errors in all the variables an efficient algorithm is developed some numerical examples are given

solutions to the quantum yang baxter equation arising from pointed bialgebras let r m m m m be a solution to the quantum yang baxter equation where m is a finite dimensional vector space over a field k we introduce a quotient ana r of the bialgebra a r constructed by fadeev reshetihkin and takhtajan whose characteristics seem to more faith fully reflect properties r possesses as a linear operator we characterize all r such that ared r is a pointed bialgebra and we determine all solutions r to the quantum yang baxter equation when ared r is pointed and dim m 2 with a few technical exceptions when k has characteristic 2 extensions of such solutions to the quantum plane are studied in this paper we study the quantum yang baxter equation from the point of view of the faddeev reshetikhin and takhtajan construction 2 to refine techniques for constructing solutions using bialgebra methods applying our methods in the two dimensional case we generate with relative ease six extensive classes of solutions in particular we find all solutions r m m m m where m is a two dimensional vector space over a field k of characteristic not 2 which are represented by an invertible upper triangular matrix with respect to a basis of the form m m n m m n n n included among these is the familiar quantum yang baxter operator

the stability of stochastic coupled systems with time delays and time varying coupling structure this paper is concerned with the pth moment exponential stability of stochastic coupled systems with time delays and time varying coupling structure sctvcs the coupling structure is time varying first second the method of graph theory has been generalized from a system established on a digraph with constant coupling structure to a digraph with time varying coupling structure successfully combining graph theory with lyapunov method a systematic method is given to construct a lyapunov function for sctvcs several pth moment exponential stability criteria are presented including a lyapunov type theorem and some sufficient criteria in the form of coefficients furthermore the theoretical conclusions are applied to the stochastic coupled oscillators with time varying coupling structure and two stability criteria are obtained finally we give two numerical examples to illustrate the effectiveness of our results

graph theory based pinning synchronization of stochastic complex dynamical networks this paper is concerned with the adaptive pinning synchronization problem of stochastic complex dynamical networks cdns based on algebraic graph theory and lyapunov theory pinning controller design conditions are derived and the rigorous convergence analysis of synchronization errors in the probability sense is also conducted compared with the existing results the topology structures of stochastic cdn are allowed to be unknown due to the use of graph theory in particular it is shown that the selection of nodes for pinning depends on the unknown lower bounds of coupling strengths finally an example on a chua s circuit network is given to validate the effectiveness of the theoretical results

on a parameterized family of twist quantum coalgebras and the bracket polynomial quantum coalgebras over a field k are structures that produce regular isotopy invariants of 1 1 tangles and twist quantum coalgebras over k are structures that produce regular isotopy invariants of knots these structures are introduced and studied in 9 in 6 and 8 certain families of quantum coalgebras and their resulting invariants of 1 1 tangles are examined in detail in this paper we use the simple coalgebra c k the dual of the algebra mn k of n x n matrices over k as a starting point for constructing twist quantum coalgebras among the twist quantum coalgebras we construct is a parameterized family related to the jones polynomial in an interesting way the jones polynomial can be computed by the normalized bracket polynomial 5 theorem 5 2 the bracket polynomial for knots in turn can be calculated from a quantum algebra structure on m2 c which is described in 5 p 580 the dual of this quantum algebra is a certain twist quantum coalgebra structure on c2 c which is discussed in 9 sect 8 thus the jones polynomial for knots can be computed from a twist quantum coalgebra structure on c2 c