supports of derivations free factorizations and ranks of fixed subgroups in free groups for f a free group of finite rank it is shown that the fixed subgroup of any set b of endomorphisms of f has rank rank f generalizing a recent result of dicks and ventura the proof involves the combinatorics of derivations of groups some related questions are examined

levels of knotting of spatial handlebodies if h is a spatial handlebody i e a handlebody embedded in the 3 sphere a spine of h is a graph s3 such that h is a regular neighbourhood of usually h is said to be unknotted if it admits a planar spine this suggests that a handlebody should be considered not very knotted if it admits spines that enjoy suitable special properties building on this remark we define several levels of knotting of spatial handlebodies and we provide a complete description of the relationships between these levels focusing our attention on the case of genus 2 we also relate the knotting level of a spatial handlebody h to classical topological properties of its complement m s3 h such as its cut number more precisely we show that if h is not highly knotted then m admits special cut systems for m and we discuss the extent to which the converse implication holds along the way we construct obstructions that allow us to determine the knotting level of several families of spatial handlebodies these obstructions are based on recent quandle coloring invariants for spatial handlebodies on the extension to the context of spatial handlebodies of tools coming from the theory of homology boundary links on the analysis of appropriate coverings of handlebody complements and on the study of the classical alexander elementary ideals of their fundamental groups

a dwindling filter line search method for unconstrained optimization in this paper we propose a new dwindling multidimensional fllter second order line search method for solving large scale unconstrained optimization problems usually the multidimensional fllter is constructed with a flxed envelope which is a strict condition for the gradient vectors a dwindling multidimensional fllter technique which is a modiflcation and improvement of the original multidimensional fllter is presented under some reasonable assumptions the new algorithm is globally convergent to a second order critical point when negative curvature direction is exploited preliminary numerical experiments on a set of cuter test problems indicate that the new algorithm is more competitive than the traditional second order line search algorithms

a nonmonotone filter trust region method for nonlinear constrained optimization in this paper we present a nonmonotone filter trust region algorithm for solving nonlinear equality constrained optimization similar to bryd omojokun class of algorithms each step is composed of a quasi normal step and a tangential step this new method has more flexibility for the acceptance of the trial step compared to the filter methods and requires less computational costs compared with the monotone methods under reasonable conditions we give the globally convergence properties numerical tests are presented that confirm the efficiency of the approach

a penalty function free line search sqp method for nonlinear programming we propose a penalty function free non monotone line search method for nonlinear optimization problems with equality and inequality constraints this method yields global convergence without using a penalty function or a filter each step is required to satisfy a decrease condition for the constraint violation as well as that for the objective function under some reasonable conditions the proposed mechanism for accepting steps also combines the non monotone technique on the decrease condition for the constraint violation which leads to flexibility and an acceptance behavior comparable with filter based methods furthermore it is shown that the proposed method can avoid the maratos effect if the search directions are improved by second order corrections soc so locally superlinear convergence is achieved we also present some numerical results which confirm the robustness and efficiency of our approach

a bundle filter method for nonsmooth convex constrained optimization for solving nonsmooth convex constrained optimization problems we propose an algorithm which combines the ideas of the proximal bundle methods with the filter strategy for evaluating candidate points the resulting algorithm inherits some attractive features from both approaches on the one hand it allows effective control of the size of quadratic programming subproblems via the compression and aggregation techniques of proximal bundle methods on the other hand the filter criterion for accepting a candidate point as the new iterate is sometimes easier to satisfy than the usual descent condition in bundle methods some encouraging preliminary computational results are also reported

a restoration free filter sqp algorithm for equality constrained optimization in this paper a trust region sequential quadratic programming algorithm with a modified filter acceptance mechanism is proposed for nonlinear equality constrained optimization the most important advantage of the proposed algorithm is its avoidance of any feasibility restoration phase a necessity in traditional filter methods we solve quadratic programming subproblems based on the well known byrd omojokun trust region method inexact solutions to these subproblems are allowed under some standard assumptions global convergence of the proposed algorithm is established numerical results show our approach is potentially useful

on the absence of mcshane type identities for the outer space abstract a remarkable result of mcshane states that for a punctured torus with a complete finite volume hyperbolic metric we have 1 e l 1 1 2 where varies over the homotopy classes of essential simple closed curves and l is the length of the geodesic representative of we prove that there is no reasonable analogue of mcshane s identity for the culler vogtmann outer space of a free group

line search filter methods for nonlinear programming local convergence a line search method is proposed for nonlinear programming using fletcher and leyffer s filter method which replaces the traditional merit function a simple modification of the method proposed in a companion paper siam j optim 16 2005 pp 1 31 introducing second order correction steps is presented it is shown that the proposed method does not suffer from the maratos effect so that fast local convergence to second order sufficient local solutions is achieved

a trust region filter method for general non linear programming filter approach is initially proposed by fletcher and leyffer in 2002 because of promising numerical results filter methods are recently attached importance to if the objective function value or the constraint violation is reduced this step is accepted by a filter which is the basic idea of the filter in this paper the filter technique is employed in a trust region algorithm in every trial step the step length is controlled by a trust region radius moreover our purpose is not to reduce the objective function and constraint violation directly to overcome some bad cases we aim to reduce the degree of constraint violation and the entry of some function and the function is a combination of the objective function and the degree of constraint violation the algorithm in this paper requires neither lagrangian multipliers nor strong decrease condition in certain conditions this method produces k t points for the original problem moreover maratos effect can be avoided for our algorithm

a lattice boltzmann scheme of the navier stokes equation on a three dimensional cuboid lattice abstract the standard lattice boltzmann method lbm for fluid flow simulation is based on a square in 2d or a cubic in 3d lattice grids recently two new lattice boltzmann schemes have been developed on a 2d rectangular grid using the mrt multiple relaxation time collision model either by adding a free parameter in the definition of moments or by extending the equilibrium moments these models satisfy all isotropy conditions and are fully consistent to the navier stokes equations here we developed a lattice boltzmann model on a 3d cuboid lattice namely a lattice grid with different grid lengths in different spatial directions we designed the moment equations derived from our mrt lbm model through the chapman enskog analysis to be fully consistent with the navier stokes equations a second order term is added to the equilibrium moments in order to not only satisfy all isotropy conditions but also to better accommodate different values of shear and bulk viscosities the form of the second order term and the coefficients of the extended equilibrium moments are determined through an inverse design process an additional benefit of the model is that the shear viscosity can be adjusted independent of the stress moment relaxation parameter thus potentially improving the numerical stability of the model the resulting cuboid mrt lbm model is then validated through benchmark simulations using the laminar channel flow the turbulent channel flow and the 3d time dependent energy cascading taylor green vortex flow the second order accuracy of the proposed model is also demonstrated the aspect ratios for numerical stability appear to be constrained at high flow reynolds numbers especially for turbulent flow simulations an aspect requiring further investigation

a filter active set algorithm for ball sphere constrained optimization problem in this paper we propose a filter active set algorithm for the minimization problem over a product of multiple ball sphere constraints by making effective use of the special structure of the ball sphere constraints a new limited memory bfgs l bfgs scheme is presented the new l bfgs implementation takes advantage of the sparse structure of the jacobian of the constraints and generates curvature information of the minimization problem at each iteration only two or three reduced linear systems are required to solve for the search direction the filter technique combined with the backtracking line search strategy ensures the global convergence and the local superlinear convergence can also be established under mild conditions the algorithm is applied to two specific applications the nearest correlation matrix with factor structure and the maximal correlation problem our numerical experiments indicate that the proposed algorithm is competitive with some recently custom designed methods for each ind

a modified sqp method with nonmonotone technique and its global convergence in this paper we propose a modified sqp method which uses neither a penalty function nor a filter for the nonlinear programming problems the proposed mechanism for accepting the trial step is carried out by a nonmonotone technique under some conditions we establish the global convergence of the algorithm some numerical results are presented to show the effectiveness of the proposed algorithm

a qp free algorithm without a penalty function or a filter for nonlinear general constrained optimization abstract in this paper we present a qp free algorithm without a penalty function or a filter for nonlinear general constrained optimization at each iteration three systems of linear equations with the same coefficient matrix are solved to yield search direction the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced there is no feasibility restoration phase in our algorithm which is necessary for filter methods the algorithm possesses global convergence as well as superlinear convergence under some mild conditions including a weaker assumption of positive definiteness finally some preliminary numerical results are reported

a lattice bgk model for the navier stokes equations based on a rectangular grid abstract in this paper starting from the standard lattice bgk lbgk equation with an extended equilibrium distribution and applying the multiscale chapman enskog ce analysis we show theoretically that the correct navier stokes n s equations can be reproduced on a non standard rectangular grid using only the bgk collision model the parameters in the extended equilibrium distribution are determined through an inverse design process this new lbgk model is then validated using two benchmark cases i e the 2d decaying taylor green vortex flow and the lid driven cavity flow the accuracy and stability of the new model are discussed the new model clearly extends the standard lbgk model as it was previously thought to be impossible to construct an lbgk model for the n s equations on a rectangular grid

global convergence of a robust filter sqp algorithm abstract we present a robust filter sqp algorithm for solving constrained optimization problems this algorithm is based on the modified quadratic programming proposed by burke to avoid the infeasibility of the quadratic programming subproblem at each iteration compared with other filter sqp algorithms our algorithm does not require any restoration phase procedure which may spend a large amount of computation the main advantage of our algorithm is that it is globally convergent without requiring strong constraint qualifications such as mangasarian fromovitz constraint qualification mfcq and the constant rank constraint qualification crcq furthermore the feasible limit points of the sequence generated by our algorithm are proven to be the kkt points if some weaker conditions are satisfied numerical results are also presented to show the efficiency of the algorithm

automorphic orbits in free groups abstract let fn be the free group of a finite rank n we study orbits orb u where u is an element of the group fn under the action of an automorphism if an orbit like that is finite we determine precisely what its cardinality can be if u runs through the whole group fn and runs through the whole group aut fn another problem that we address here is related to whitehead s algorithm that determines whether or not a given element of a free group of finite rank is an automorphic image of another given element it is known that the first part of this algorithm reducing a given free word to a free word of minimum possible length by elementary whitehead automorphisms is fast of quadratic time with respect to the length of the word on the other hand the second part of the algorithm applied to two words of the same minimum length was always considered very slow we give here an improved algorithm for the second part and we believe this algorithm always terminates in polynomial time with respect to the length of the words we prove that this is indeed the case if the free group has rank 2

a robust sequential quadratic programming method the sequential quadratic programming method developed by wilson han and powell may fail if the quadratic programming subproblems become infeasible or if the associated sequence of search directions is unbounded this paper considers techniques which circumvent these difficulties by modifying the structure of the constraint region in the quadratic programming subproblems furthermore questions concerning the occurrence of an unbounded sequence of multipliers and problem feasibility are also addressed

a new filter levenberg marquardt method with disturbance for solving nonlinear complementarity problems recently filter methods are extensively studied to handle nonlinear programming problems because of good numerical results filter techniques are attached importance to the nonlinear complementarity problem can be reformulated as the least l 2 norm solution of an optimization problem in this paper basing on the filter technique and the new smoothing function we present a new filter levenberg marquardt method for solving the equation system j z k m z k l ki dz k b kz with the disturbance b kz under the assumption that the lever set of the problem is compact we prove its global convergence

a filter variable metric method for nonsmooth convex constrained optimization we propose an algorithm for solving nonsmooth convex constrained problems which combines the ideas of the variable metric methods with the filter strategy for evaluating candidate points the resulted algorithm inherits some attractive features from both approaches on the one hand the time consuming quadratic programming sub problems do not need to be solved on the other hand the dominance concept of multiobjective optimization was used and the new iterate must satisfy so called filter criterion some encouraging preliminary computational results are reported

designing correct fluid hydrodynamics on a rectangular grid using mrt lattice boltzmann approach while the lattice boltzmann method lbm has become a powerful numerical approach for solving complex flows the standard lattice boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions for inhomogeneous and anisotropic flows it is desirable to have a lbm model that utilizes a rectangular grid there were two previous attempts to extend the multiple relaxation time mrt lbm to a rectangular lattice grid in 2d however the resulting hydrodynamic momentum equation was not fully consistent with the navier stokes equation due to anisotropy of the transport coefficients in the present work a new mrt model with an additional degree of freedom is developed in order to match precisely the navier stokes equation when a rectangular lattice grid is used we first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the chapman enskog procedure then an additional adjustable parameter that governs the relative orientation in the energy normal stress subspace is introduced it is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients thus the exact navier stokes equation can be derived on a rectangular grid our theoretical findings are confirmed by numerical solutions using three two dimension benchmark problems i e the channel flow the cavity flow and the decaying taylor green vortex flow the numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters

brief paper two nonlinear optimization methods for black box identification compared in this paper two nonlinear optimization methods for the identification of nonlinear systems are compared both methods estimate the parameters of e g a polynomial nonlinear state space model by means of a nonlinear least squares optimization of the same cost function while the first method does not estimate the states explicitly the second method estimates both states and parameters adding an extra constraint equation both methods are introduced and their similarities and differences are discussed utilizing simulation data the unconstrained method appears to be faster and more memory efficient but the constrained method has a significant advantage as well it is robust for unstable systems of which bounded input output data can be measured e g a system captured in a stabilizing feedback loop both methods have successfully been applied on real life measurement data

a filter method for solving nonlinear complementarity problems filter methods are extensively studied to handle nonlinear programming problems recently because of good numerical results filter techniques are attached importance to in this paper filter approaches are employed to tackle nonlinear complementarity problems ncps firstly ncp conditions are transformed into a nonlinear programming problem then to obtain a trial step the corresponding nonlinear programming problems are solved by some existing strategies moreover filter criterion is utilized to evaluate a trial iterate the purpose in this paper is to employ filter approaches to attack ncps in essence multi objective view is utilized to attack ncps because the idea of filter methods stems from multi objective problems furthermore a new filter method based on the special two objects which differs from others is brought forward moreover maratos effects are overcome in our new filter approach by weakening acceptable conditions

a trust region algorithm combining line search filter method with lagrange merit function for nonlinear constrained optimization this paper presents a trust region algorithm which employs line search filter technique with lagrange merit function for solving nonlinear equality constrained programming at the current iteration the general full trust region subproblem is decomposed into a pair of trust region subproblems in normal and tangential subspaces the trial step is given by solving these two trust region subproblems then different from traditional trust region method in which the next iterate is determined by the ratio of the actual reduction to the predicted reduction the step size is decided by interior backtracking line search together with filter method consequently the expensive computation raised by resolving trust region subproblem many times to determine a new iteration point in traditional trust region method can be reduced and the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique the new method retains the global convergence to the first order critical points under some reasonable assumptions without using a merit function meanwhile by using lagrange function in the filter the method can overcome maratos effect without using second order correction step and hence the superlinear local convergence is achieved the preliminary numerical results are reported to show effectiveness of the proposed algorithm

a semismooth newton method with multidimensional filter globalization for l_1 optimization due to their property of enhancing the sparsity of solutions l 1 regularized optimization problems have developed into a highly dynamic research area with a wide range of applications we present a class of methods for l 1 regularized optimization problems that are based on a combination of semismooth newton steps a filter globalization and shrinkage thresholding steps a multidimensional filter framework is used to control the acceptance and to evaluate the quality of the semismooth newton steps if the current newton iterate is rejected a shrinkage thresholding based step with quasi armijo stepsize rule is used instead global convergence and transition to local q superlinear convergence for both convex and nonconvex objective functions are established we present numerical results and comparisons with several state of the art methods that show the efficiency and competitiveness of the proposed method

a dwindling filter inexact projected hessian algorithm for large scale nonlinear constrained optimization in this paper we propose a dwindling filter inexact projected hessian algorithm for solving large scale nonlinear constrained optimization for large scale applications inexact projected hessian algorithm is needed to get search direction by solving one or more linear systems approximately using iterative linear algebra techniques the envelope of the dwindling filter becomes thinner and thinner as the step size approaches zero so that the new filter has more flexibility for the acceptance of the trial step compared with traditional filter under mild conditions global convergence and local superlinear convergence rate are obtained the numerical experiments are reported to show the effectiveness of the proposed algorithm for large scale problems

local convergence of a trust region algorithm with line search filter technique for nonlinear constrained optimization a trust region algorithm in association with line search filter technique for solving nonlinear equality constrained programming is proposed in this paper in the current iteration the trial step providing sufficient descent is generated by solving a corresponding trust region subproblem then the step size is decided by backtracking line search together with filter technique to obtain the next iteration point the advantage of this method is that resolving trust region subproblem many times to determine a new iteration point in traditional trust region method can be avoided and hence the expensive computation can be lessened and the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique second order correction steps are introduced in the proposed algorithm to overcome maratos effect convergence analysis shows that fast local convergence can be achieved under some mild assumptions the preliminary numerical results are reported

a trust region method for solving generalized complementarity problems based on a semismooth equation reformulation using fischer s function a trust region algorithm is proposed for solving the generalized complementarity problem gcp the algorithm uses a generalized jacobian of the function involved in the semismooth equation and adopts the squared natural residual of the semismooth equation as a merit function the proposed algorithm is applicable to the nonlinear complementarity problem because the latter problem is a special case of the gcp global convergence and under a nonsingularity assumption local q superlinear or quadratic convergence of the algorithm are established moreover calculation of a generalized jacobian is discussed and numerical results are presented

optimization by direct search new perspectives on some classical and modern methods direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis nonetheless users remained loyal to these methods most of which were easy to program some of which were reliable in the past fifteen years these methods have seen a revival due in part to the appearance of mathematical analysis as well as to interest in parallel and distributed com puting this review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results the underlying principles allow general ization to handle bound constraints and linear constraints we also discuss extensions to problems with nonlinear constraints

a filter algorithm for nonlinear systems of equalities and inequalities abstract in this paper we propose a filter algorithm for nonlinear systems of equalities and inequalities in the algorithm the systems of nonlinear equalities and inequalities are transformed into a nonlinear programming problem the new algorithm uses the non monotone technique in conjunction with filter idea and a global line search strategy that ensures convergence from any starting point under mild conditions global convergence and local superlinear convergence rate are obtained numerical results demonstrate that the new algorithm is effective

global convergence of a general filter algorithm based on an efficiency condition of the step in this work we discuss global convergence of a general filter algorithm that depends neither on the definition of the forbidden region which can be given by the original or slanting filter rule nor on the way in which the step is computed this algorithm basically consists of calculating a point not forbidden by the filter from the current point assuming that this step must be efficient in the sense that near a feasible non stationary point the decrease in the objective function is relatively large we prove the global convergence of the algorithm we also discuss that such a condition is satisfied if the step is computed by the sqp or inexact restoration methods for sqp we present a general proof of this result that is valid for both the original and the slanting filter criterion in order to compare the performance of the general filter algorithm according to the method used to calculate the step and the filter rule regarded we present numerical experiments performed with problems from cuter collection

a trust region sqp filter method for nonlinear second order cone programming in this paper we consider the nonlinear second order cone programming problem by combining an sqp method and filter technique we present a trust region sqp filter method for solving this problem the proposed algorithm avoids using the classical merit function with penalty term furthermore under standard assumptions we prove that the iterative sequence generated by the presented algorithm converges globally preliminary numerical results indicate that the algorithm is promising

global convergence of slanting filter methods for nonlinear programming in this paper we present a general algorithm for nonlinear programming which uses a slanting filter criterion for accepting the new iterates independently of how these iterates are computed we prove that all accumulation points of the sequence generated by the algorithm are feasible computing the new iterates by the inexact restoration method we prove stationarity of all accumulation points of the sequence

a derivative free filter method for solving nonlinear complementarity problems in this work nonlinear complementarity problems ncps are considered some ncps which come from practice have no derivatives or it is very difficult to obtain their derivatives derivative free methods are hence considered generalized pattern search gps method as a kind of derivative free method plays a very significant role we combine generalized pattern search method with filter method to attack ncps because one can analyze the theory of generalized pattern search filter method without sufficient reduction conditions and avoid using of derivatives some interesting results are obtained in this work without sufficient reduction conditions furthermore generalized pattern search filter method is efficient to some special problems

on the global convergence of a filter sqp algorithm a mechanism for proving global convergence in sqp filter methods for nonlinear programming nlp is described such methods are characterized by their use of the dominance concept of multiobjective optimization instead of a penalty parameter whose adjustment can be problematic the main point of interest is to demonstrate how convergence for nlp can be induced without forcing sufficient descent in a penalty type merit function the proof relates to a prototypical algorithm within which is allowed a range of specific algorithm choices associated with the hessian matrix representation updating the trust region radius and feasibility restoration

a new penalty free type algorithm based on trust region techniques abstract in this paper we propose a new penalty free type method for nonlinear equality constrained problems the new algorithm uses trust region framework and feasibility safeguarding technique moreover it has no choice of penalty parameter and penalty function as a merit function and it does not use the filter technique to avoid the penalty function either we analyze the global convergence of the main algorithm under the standard assumptions the preliminary numerical tests are reported

on the global convergence of an slp filter algorithm that takes eqp steps a global convergence proof is presented for a class of trust region filter type methods for nonlinear programming such methods are characterized by their use of the dominance concept of multiobjective optimization instead of a penalty parameter whose adjustment can be problematic the methods are based on successively solving linear programming subproblems for which effective software is readily available the methods also permit the use of steps calculated on the basis of an equality constrained quadratic programming model which enables rapid convergence to take place for problems in which second order information is important the proof technique is presented in a fairly general context allowing a range of specific algorithm choices associated with choosing the quadratic model updating the trust region radius and with feasibility restoration

dealing with singularities in nonlinear unconstrained optimization we propose a new trust region based optimization algorithm for solving unconstrained nonlinear problems whose second derivatives matrix is singular at a local solution we give a theoretical characterization of the singularity in this context and we propose an iterative procedure which allows to identify a singularity in the objective function during the course of the optimization algorithm and artificially adds curvature to the objective function numerical tests are performed on a set of unconstrained nonlinear problems both singular and non singular results illustrate the significant performance improvement compared to classical trust region and filter algorithms proposed in the literature the approach is also shown to be competitive with tensor methods in terms of efficiency while reaching a higher level of robustness

global convergence of filter methods for nonlinear programming we present a general filter algorithm that allows a great deal of freedom in the step computation each iteration of the algorithm consists basically in computing a point which is not forbidden by the filter from the current point we prove its global convergence assuming that the step must be efficient in the sense that near a feasible nonstationary point the reduction of the objective function is large we show that this condition is reasonable by presenting two classical ways of performing the step which satisfy it in the first one the step is obtained by the inexact restoration method of martinez and pilotta in the second the step is computed by sequential quadratic programming

on the superlinear local convergence of a penalty free method for nonlinear semidefinite programming abstract this paper is concerned with a sequentially semidefinite programming ssdp algorithm for solving nonlinear semidefinite programming problems nlsdp which does not use a penalty function or a filter this method inspired by the classic sqp method calculates a trial step by a quadratic semidefinite programming subproblem at each iteration the trial step is determined such that either the value of the objective function or the measure of constraint violation is sufficiently reduced in order to guarantee global convergence the measure of constraint violation in each iteration is required not to exceed a progressively decreasing limit we prove the global convergence properties of the algorithm under mild assumptions we also analyze the local behaviour of the proposed method while using a second order correction strategy to avoid maratos effect we prove that under the strict complementarity and the strong second order sufficient conditions with the sigma term the rate of local convergence is superlinear finally some numerical results with nonlinear semidefinite programming formulation of control design problem with the data contained in c o m p l e i b are given

a study of the difference of convex approach for solving linear programs with complementarity constraints this paper studies the difference of convex dc penalty formulations and the associated difference of convex algorithm dca for computing stationary solutions of linear programs with complementarity constraints lpccs we focus on three such formulations and establish connections between their stationary solutions and those of the lpcc improvements of the dca are proposed to remedy some drawbacks in a straightforward adaptation of the dca to these formulations extensive numerical results including comparisons with an existing nonlinear programming solver and the mixed integer formulation are presented to elucidate the effectiveness of the overall dc approach

nonlinear programming and nonsmooth optimization by successive linear programming methods are considered for solving nonlinear programming problems using an exactl1 penalty function lp like subproblems incorporating a trust region constraint are solved successively both to estimate the active set and to provide a foundation for proving global convergence in one particular method second order information is represented by approximating the reduced hessian matrix and coleman conn steps are taken a criterion for accepting these steps is given which enables the superlinear convergence properties of the coleman conn method to be retained whilst preserving global convergence and avoiding the maratos effect the methods generalize to solve a wide range of composite nonsmooth optimization problems and the theory is presented in this general setting a range of numerical experiments on small test problems is described

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

an sqp filter method for inequality constrained optimization and its global convergence in this paper we combine the filter technique with a modified sequential quadratic programming sqp method the optimization solution is obtained by reducing step length which is obtained by an exact linear search furthermore this method can start with an infeasible initial point the method uses a filter to promote global convergence

the algebraic entropy of the special linear character automorphisms of a free group on two generators in this note we establish a connection between the dynamical de gree or algebraic entropy of a certain class of polynomial automorphisms of r 3 and the maximum topological entropy of the action when restricted to compact invariant subvarieties indeed when there is no cancellation of lead ing terms in the successive iterates of the polynomial automorphism the two quantities are equal in general however the algebraic entropy overestimates the topological entropy these polynomial automorphisms arise as extensions of mapping class actions of a punctured torus s on the relative su 2 character varieties of s embedded inr 3 it is known that the topological entropy of these mapping class actions is maximized on the relative character variety comprised of reducible characters those whose boundary holonomy is 2 here we cal culate the algebraic entropy of the induced polynomial automorphisms on the character varieties and show that it too solely depends on the topology of s

avoiding the maratos effect by means of a nonmonotone line search ii inequality constrained problems feasible iterates when solving inequality constrained optimization problems via sequential quadratic programming sqp it is potentially advantageous to generate iterates that all satisfy the constraints all quadratic programs encountered are then feasible and there is no need for a surrogate merit function feasibility of the successive iterates is in fact required in many contexts such as in real time applications or when the objective function is not defined outside the feasible set it has recently been shown that this is indeed possible by means of a suitable perturbation of the original sqp iteration without losing superlinear convergence in this context the well known maratos effect is compounded by the possible infeasibility of the full step of one even close to a solution these difficulties have been accommodated by making use of a suitable modification of a bending technique proposed by mayne and polak requiring evaluation of the constraints function at an auxiliary point at each iteration in part i

every group is the outer automorphism group of an hnn extension of a fixed triangle group abstract fix an equilateral triangle group t i a b a i b i a b i with i 6 arbitrary our main result is for every presentation p of every countable group q there exists an hnn extension t p of t i such that out t p q we construct the hnn extensions explicitly and examples are given the class of groups constructed have nice categorical and residual properties in order to prove our main result we give a method for recognising malnormal subgroups of small cancellation groups and we introduce the concept of malcharacteristic subgroups

analysis of generalized pattern searches this paper contains a new convergence analysis for the lewis and torczon generalized pattern search gps class of methods for unconstrained and linearly constrained optimization this analysis is motivated by a desire to understand the successful behavior of the algorithm under hypotheses that are satisfied by many practical problems specifically even if the objective function is discontinuous or extended valued the methods find a limit point with some minimizing properties simple examples show that the strength of the optimality conditions at a limit point depends not only on the algorithm but also on the directions it uses and on the smoothness of the objective at the limit point in question the contribution of this paper is to provide a simple convergence analysis that supplies detail about the relation of optimality conditions to objective smoothness properties and to the defining directions for the algorithm and it gives previous results as corollaries

a trust region sqp method without a penalty or a filter for nonlinear programming in this paper we present a new trust region sqp algorithm for nonlinear programming this method avoids using a penalty function nor a filter and instead establishes a new step acceptance mechanism under some reasonable assumptions the method can be proved to be globally convergent to a kt point preliminary numerical experiments are presented that show the potential efficiency of the new approach

primitive almost primitive test and δ primitive elements of free algebras with the nielsen schreier property abstract we study generalized primitive elements of free algebras of finite ranks with the nielsen schreier property and their automorphic orbits a primitive element of a free algebra is an element of some free generating set of this algebra almost primitive elements are not primitive elements which are primitive in any proper subalgebra primitive elements are elements whose partial derivatives generate the same one sided ideal of the universal multiplicative envelope algebra of a free algebra as the set of free generators generate we prove that an endomorphism preserving an automorphic orbit of a nonzero element of a free algebra of rank two is an automorphism an algorithm to determine test elements of free algebras of rank two is described a series of almost primitive elements is constructed and new examples of test elements are given we prove that if the rank n of the free lie algebra l is even n 2m then any primitive element of l is an automorphic image of the element w x1 x2 x2m 1 x2m there are no primitive elements of l if n is odd and the group of automorphisms of the algebra l acts transitively on the set of all primitive elements

a nonmonotone filter sqp method local convergence and numerical results the work by gould loh and robinson siam j optim 24 2014 pp 175 209 established global convergence of a new filter line search method for finding local first order solutions to nonlinear and nonconvex constrained optimization problems a key contribution of that work was that the search direction was computed using the same procedure during every iteration from subproblems that were always feasible and computationally tractable this contrasts previous filter methods that require a separate restoration phase based on subproblems solely designed to reduce infeasibility in this paper we present a nonmonotone variant of our previous algorithm that inherits the previously established global convergence property in addition we establish local superlinear convergence of the iterates and provide the results of numerical experiments the numerical tests validate our method and highlight an interesting numerical trade off between accepting more on average lower quality steps versus fewer on avera

palindromic primitives and palindromic bases in the free group of rank two abstract the present paper records more details of the relationship between primitive elements and palindromes in f 2 the free group of rank two we characterize the conjugacy classes of palindromic primitive elements as those in which cyclically reduced words have odd length we identify large palindromic subwords of certain primitives in conjugacy classes which contain cyclically reduced words of even length we show that under obvious conditions on exponent sums pairs of palindromic primitives form palindromic bases for f 2 further we note that each cyclically reduced primitive element is either a palindrome or the concatenation of two palindromes

on the local convergence of quasi newton methods for constrained optimization we consider the application of a general class of quasi newton methods to the solution of the classical equality constrained nonlinear optimization problem specifically we develop necessary and sufficient conditions for the q superlinear convergence of such methods and present a companion linear convergence theorem the essential conditions relate to the manner in which the hessian of the lagrangian function is approximated

global convergence of a nonmonotone filter method for equality constrained optimization abstract in this paper we present a global convergence theory for a class of nonmonotone filter trust region methods at each iteration the trial step is decomposed into a quasi normal step and a tangential step comparable to the traditional filter and monotone methods the new approach is more flexible and less computational scale under some reasonable conditions we show that there exists at least one accumulate point of the sequence of iterates that is a kkt point

global and local convergence of a penalty free method for nonlinear programming we present a class of trust region algorithms that do not use any penalty function or a filter for nonlinear equality constrained optimization in each iteration the infeasibility is controlled by a progressively decreasing upper limit and trial steps are computed by a byrd omojokun type trust region strategy measures of optimality and infeasibility are computed whose relationship serves as a criterion on which the algorithm decides which one to focus on improving as a result the algorithm keeps a balance between the improvements on optimality and feasibility even if no restoration phase which is required by filter methods is used the framework of the algorithm ensures the global convergence without assuming regularity or boundedness on the iterative sequence by using a second order correction strategy marato s effect is avoided and fast local convergence is shown the preliminary numerical results are reported

a derivative free filter algorithm for nonlinear complementarity problem recently so called derivative free methods have attracted much attention which do not require computation of derivatives of function and are particularly suitable for problems which the derivatives are not available or are extremely expensive to compute this paper presents a new derivative free algorithm for nonlinear complementarity problem which makes use of the efficiency of the filter technique the algorithm is shown under the monotonicity assumption to globally converge to the solution of the nonlinear complementarity problem the numerical results show the algorithm is feasible

comment on rectangular lattice boltzmann method it is shown both analytically and numerically that the suggested lattice boltzmann model on rectangular grids j g zhou phys rev e 81 026705 2010 leads to anisotropic dissipation of fluid momentum and thus does not recover the navier stokes equations hence it cannot be used for the simulation of hydrodynamics

a modified slp algorithm and its global convergence this paper concerns a filter technique and its application to the trust region method for nonlinear programming nlp problems we used our filter trust region algorithm to solve nlp problems with equality and inequality constraints instead of solving nlp problems with just inequality constraints as was introduced by fletcher et al r fletcher s leyffer ph l toint on the global converge of an slp filter algorithm report na 183 department of mathematics dundee university dundee scotland 1999 we incorporate this filter technique into the traditional trust region method such that the new algorithm possesses nonmonotonicity unlike the tradition trust region method our algorithm performs a nonmonotone filter technique to find a new iteration point if a trial step is not accepted under mild conditions we prove that the algorithm is globally convergent

a hydrodynamically consistent mrt lattice boltzmann model on a 2d rectangular grid a multiple relaxation time mrt lattice boltzmann lb model on a d2q9 rectangular grid is designed theoretically and validated numerically in the present work by introducing stress components into the equilibrium moments this mrt lb model restores the isotropy of diffusive momentum transport at the macroscopic level or in the continuum limit leading to moment equations that are fully consistent with the navierstokes equations the model is derived by an inverse design process which is described in detail except one moment associated with the energy square all other eight equilibrium moments can be theoretically and uniquely determined the model is then carefully validated using both the two dimensional decaying taylorgreen vortex flow and lid driven cavity flow with different grid aspect ratios the corresponding results from an earlier model bouzidi et al 2001 28 are also presented for comparison the results of bouzidi et al s model show problems associated with anisotropy of viscosity coefficients while the present model exhibits full isotropy and is accurate and stable

enumerating palindromes and primitives in rank two free groups abstract let f be a free group of rank two an element of f is primitive if it along with another group element generates the group if f a b then a word w a b in a and b is a palindrome if it reads the same forwards and backwards it is known that in a rank two free group for any fixed set of two generators a primitive element will be conjugate either to a palindrome or to the product of two palindromes but known iteration schemes for all primitive words give only a representative for the conjugacy class here we derive a new iteration scheme that gives either the unique palindrome in the conjugacy class or expresses the word as a unique product of two unique palindromes that have already appeared in the scheme we denote these words by e p q where p q is rational number expressed in lowest terms we prove that e p q is a palindrome if pq is even and the unique product of two unique palindromes if pq is odd we prove that the pair x y or x 1 y 1 generates the group if and only if x is conjugate to e p q and y is conjugate to e r s where p s r q 1 this improves a previously known result that held only for pq and rs both even the derivation of the enumeration scheme also gives a new proof of the known results about primitive words

on the superlinear local convergence of a filter sqp method transition to superlinear local convergence is shown for a modified version of the trust region filter sqp method for nonlinear programming introduced by fletcher leyffer and toint 8 hereby the original trust region sqp steps can be used without an additional second order correction the main modification consists in using the lagrangian function value instead of the objective function value in the filter together with an appropriate infeasibility measure moreover it is shown that the modified trust region filter sqp method has the same global convergence properties as the original algorithm in 8

three modeling paradigms in mathematical programming celebrating the sixtieth anniversary since the zeroth international symposium on mathematical programming was held in 1949 this paper discusses several promising paradigms in mathematical programming that have gained momentum in recent years but have yet to reach the main stream of the field these are competition dynamics and hierarchy the discussion emphasizes the interplay between these paradigms and their connections with existing subfields including disjunctive equilibrium and nonlinear programming and variational inequalities we will describe the modeling approaches mathematical formulations and recent results of these paradigms and sketch some open mathematical and computational challenges arising from the resulting optimization and equilibrium problems our goal is to elucidate the need for a systematic study of these problems and to inspire new research in the field

a modified sqp filter method and its global convergence for current sequential programming sqp type algorithms there exist two problems one is that there are many quadratic programming subproblems are needed to be solved per iteration the other is that the search direction may be unbounded and caused the sequence to be divergent in this paper we presented a modified sqp filter method based on the modified quadratic subproblem proposed in zhou g l zhou a modified sqp method and its global convergence j global optim 11 1997 193 205 this method has no demand on the initial point and need not using a penalty parameter which could be problematic to obtain what is more the subproblem is feasible at each iterate point under some conditions the global convergence property is obtained

on the dynamics and the fixed subgroup of a free group automorphism on considere des automorphismes f n f n ou f n f a 1 a n est le groupe libre de base a 1 a 2 a n n 2 on compose un champ vectoriel sur un graphe d on introduit des aretes repulsives attractives et des points fixes a l infini et on etudie la dynamique resultante