stability in the presence of degeneracy and error estimation given an approximation to a local minimizer to a nonlinear optimization problem and to associated multipliers we obtain a tight error estimate in terms of the violation of the first order conditions our results apply to degenerate optimization problems where independence of the active constraint gradients and strict complementarity can be violated

tdgl and mkdv equations for jamming transition in the lattice models of traffic abstract the lattice models of traffic are proposed to describe the jamming transition in traffic flow on a highway in terms of thermodynamic terminology of phase transitions and critical phenomena they are the lattice versions of the hydrodynamic model of traffic two lattice models are presented one is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other is the difference equation in which both time and space variables are discrete we apply the linear stability theory and the nonlinear analysis to the lattice models it is shown that the time dependent ginzburg landau tdgl equation is derived to describe the traffic flow near the critical point a thermodynamic theory is formulated for describing the phase transitions and critical phenomena it is also shown that the perturbed modified korteweg de vries mkdv equation is derived to describe the traffic jam

modifying sqp for degenerate problems most local convergence analyses of the sequential quadratic programming sqp algorithm for nonlinear programming make strong assumptions about the solution namely that the active constraint gradients are linearly independent and that there are no weakly active constraints in this paper we establish a framework for variants of sqp that retain the characteristic superlinear convergence rate even when these assumptions are relaxed proving general convergence results and placing some recently proposed sqp variants in this framework we discuss the reasons for which implementations of sqp often continue to exhibit good local convergence behavior even when the assumptions commonly made in the analysis are violated finally we describe a new algorithm that formalizes and extends standard sqp implementation techniques and we prove convergence results for this method also

v subdifferentials of convex operators abstract for any convex operator from a convex set c of a topological vector space e into another one f endowed with a convex cone f a notion of v subdifferential v a of at a c is introduced although it is equivalent to the notion of e sub differential when f r it enjoys many important properties which are not satisfied by the e subdifferential whenever int f o the nonvacuity of v a is proved whenever v is a neighbourhood of zero in f and belongs to a large class of mappings analogous to the class of lower semicontinuous real valued convex functions other properties of v subdifferentials are studied and applications to differentiability of are made

stabilized sequential quadratic programming for optimization and a stabilized newton type method for variational problems the stabilized version of the sequential quadratic programming algorithm ssqp had been developed in order to achieve fast convergence despite possible degeneracy of constraints of optimization problems when the lagrange multipliers associated to a solution are not unique superlinear convergence of ssqp had been previously established under the strong second order sufficient condition for optimality without any constraint qualification assumptions we prove a stronger superlinear convergence result than the above assuming the usual second order sufficient condition only in addition our analysis is carried out in the more general setting of variational problems for which we introduce a natural extension of ssqp techniques in the process we also obtain a new error bound for karush kuhn tucker systems for variational problems that holds under an appropriate second order condition

linear stability and nonlinear analyses of traffic waves for the general nonlinear car following model with multi time delays abstract in this paper the general nonlinear car following model with multi time delays is investigated in order to describe the reactions of vehicle to driving behavior platoon stability and string stability criteria are obtained for the general nonlinear car following model burgers equation and korteweg de vries kdv equation and their solitary wave solutions are derived adopting the reductive perturbation method we investigate the properties of typical optimal velocity model using both analytic and numerical methods which estimates the impact of delays about the evolution of traffic congestion the numerical results show that time delays in sensing relative movement is more sensitive to the stability of traffic flow than time delays in sensing host motion

stability analysis of the mixed traffic flow of cars and trucks using heterogeneous optimal velocity car following model abstract real world traffic flow usually contains a mixture of passenger vehicles pv and heavy vehicles hv in this paper the four types of car truck following combinations are considered the car following car case car following truck case truck following car case and truck following truck case the effect of different combinations on the stability of traffic flow is explored by converting the original bando s optimal velocity ov model to a heterogeneous form a new linear stability analysis method that can derive the stability criterion of the heterogeneous traffic flow mixed by cars and trucks is introduced moreover the effect of the proportions of the four car truck following combinations on traffic flow is examined through the trajectory analysis it concludes that the linear stability of the car truck mixed traffic flow is determined more by the proportions of the different car truck following scenarios rather than the numbers of the cars and trucks moreover cars and trucks can both stabilize and destabilize traffic flow depending on the density of the traffic flow and the parameters of the heterogeneous ov model

kdv and kink antikink solitons in car following models abstract the jams in the congested traffic are related with various density waves which might be governed by the nonlinear wave equations such as the korteweg de vries kdv equation the burgers equation and the modified korteweg de vries mkdv equation three different versions of optimal velocity models are examined the stability conditions of the models are obtained by using the linear stability theory the kdv equation near the neutral stability line and the mkdv equation around the critical point are derived by applying the reductive perturbation method respectively the traffic jams could be thus described by the kdv and kink antikink soliton solutions for the two kinds of equations the general solutions are given for which can lead to specific solutions in previous work moreover they are applied to solve a new model the full velocity difference model and the corresponding kdv and kink antikink soliton solutions could be quickly obtained which demonstrates the general solutions presented herein are useful

local behavior of an iterative framework for generalized equations with nonisolated solutions an iterative framework for solving generalized equations with nonisolated solutions is presented for generalized equations with the structure where is a multifunction and f is single valued the framework covers methods that at each step solve subproblems of the type the multifunction approximates f around s besides a condition on the quality of this approximation two other basic assumptions are employed to show q superlinear or q quadratic convergence of the iterates to a solution a key assumption is the upper lipschitz continuity of the solution set map of the perturbed generalized equation moreover the solvability of the subproblems is required conditions that ensure these assumptions are discussed in general and by means of several applications they include monotone mixed complementarity problems karush kuhn tucker systems arising from nonlinear programs and nonlinear equations particular results deal with error bounds and upper lipschitz continuity properties for these problems

an algorithm for degenerate nonlinear programming with rapid local convergence this paper describes and analyzes an algorithmic framework for solving nonlinear programming problems in which strict complementarity conditions and constraint qualifications are not necessarily satisfied at a solution the framework is constructed from three main algorithmic ingredients the first is any conventional method for nonlinear programming that produces estimates of the lagrange multipliers at each iteration the second is a technique for estimating the set of active constraint indices the third is a stabilized lagrange newton algorithm with rapid local convergence properties results concerning rapid local convergence and global convergence of the proposed framework are proved the approach improves on existing approaches in that less restrictive assumptions are needed for convergence and or the computational workload at each iteration is lower

kink soliton characterizing traffic congestion we study traffic congestion by analyzing a one dimensional traffic flow model developing an asymptotic method to investigate the long time behavior near a critical point we derive the modified korteweg de vries mkdv equation as the lowest order model there is an infinite number of kink solitons to the mkdv equation while it has been found by numerical simulations that the kink pattern arising in traffic congestion is uniquely determined irrespective of initial conditions in order to resolve this selection problem we consider higher order corrections to the mkdv equation and find that there is a kink soliton that can deform continuously with the perturbation represented by the addition of these corrections with numerical confirmation we show that this continuously deformable kink soliton characterizes traffic congestion we also discuss the relationship between traffic congestion and the slugging phenomenon in granular flow

a new variational result for quasi newton formulae the recent measure function of byrd and nocedal siam j numer anal 26 1989 pp 727 739 is considered and simple proofs of some of its properties are given it is then shown that the bfgs and dfp formulae satisfy a least change property with respect to this new measure

exact solutions for a discrete system arising in traffic flow this paper concerns wave propagation in a discrete nonlinear system of equations proposed and studied by g f newell as a model for car following in traffic flow in particular newell found exact solutions for shock waves and related phenomena here exact solutions representing periodic waves and solitary waves are obtained the method relates travelling wave solutions to the toda and kac van moerbeke discrete systems in this and other ways much of the interest is in the general phenomena possible in discrete systems here including also a time lag rather than in just the specific traffic flow setting

continuous affine support mappings for convex operators abstract we investigate the problem of existence of continuous affine resp linear support mappings for convex resp sublinear partially defined operators we prove that a weakly borel measurable convex operator defined on a closed convex subset of a locally convex frechet space with values in an ordered locally convex vector space with the least upper bound property and an order unit inducing the topology in fact has continuous affine support mappings we give an example indicating that the order unit being present is essential a step towards our result is provided by a variant of the sandwich theorem obtained for the case of weakly borel measurable convex and concave operators finally we obtain necessary and sufficient conditions for the existence of a continuous affine support mapping h for a convex operator such that h x 0 x 0 holds for a fixed point x 0 in terms of the upper directional derivate x 0 for at x 0

modified kdv equation for jamming transition in the continuum models of traffic abstract continuum models of traffic are proposed to describe the jamming transition in traffic flow on a highway they are the simplified versions of the hydrodynamic model of traffic two continuum models are presented one is described by the partial differential equations and the other is the discrete lattice version the linear stability theory and the nonlinear analysis are applied to the continuum models the modified korteweg de vries equation kdv near the critical point is derived using the reduction perturbation method it is shown that the jamming transition and the density wave in the congested traffic flow are described by the modified kdv equation the solutions of the kdv equations obtained from the two models are compared with that of the optimal velocity model car following model

conjugate convex operators convex mappings from a locally convex space x into f f are considered where f is an ordered topological vector space and an arbitrary greatest element adjoined to f in view of applications to the polarity theory of convex operators the possibility is investigated of representing a convex mapping taking values in f as a supremum of continuous affine mappings

orthogonal projections on convex sets for newton like methods this paper develops the fixed almost least change secant methods for solving of nonlinear problems the presented results generalize and extend some results given by dennis and walker siam j numer anal 18 1981 pp 949 987 among other things multilevel update algorithms are described

continuity and differentiability properties of convex operators this paper provides some theorems on the generic differentiability of convex operators between topological vector spaces these results are applied to give new conditions for subgradients of convex operators to be non empty and well behaved limiting examples are given

time dependent ginzburg landau equation in a car following model considering the driver s physical delay abstract in this paper an extended car following model considering the delay of the driver s response in sensing headway is proposed to describe the traffic jam it is shown that the stability region decreases when the driver s physical delay in sensing headway increases the phase transition among the freely moving phase the coexisting phase and the uniformly congested phase occurs below the critical point by applying the reductive perturbation method we get the time dependent ginzburg landau tdgl equation from the car following model to describe the transition and critical phenomenon in traffic flow we show the connection between the tdgl equation and the mkdv equation describing the traffic jam

numerical simulation of soliton and kink density waves in traffic flow with periodic boundaries abstract the soliton and kink antikink density waves are simulated with periodic boundaries by adding perturbation in the initial condition on single lane road based on a car following model they are reproduced in the form of the space time evolution of headway both of which propagate backwards it is found that the solitons appear only near the neutral stability line regardless of the boundary conditions and they exhibit upward form when the initial headway is smaller than the safety distance otherwise they exhibit downward form comparison is made between the numerical and analytical results about the amplitude of kink antikink wave and the underlying mechanism is analyzed besides it is indicated that the maximal current of traffic flow increases with decreasing safety distance the numerical simulation shows a good agreement with the analytical results

a quasi newton strategy for the ssqp method for variational inequality and optimization problems the quasi newton strategy presented in this paper preserves one of the most important features of the stabilized sequential quadratic programming method the local convergence without constraint qualifications assumptions it is known that the primal dual sequence converges quadratically assuming only the second order sufficient condition in this work we show that if the matrices are updated by performing a minimization of a bregman distance which includes the classic updates the quasi newton version of the method converges superlinearly without introducing further assumptions also we show that even for an unbounded lagrange multipliers set the generated matrices satisfies a bounded deterioration property and the dennis more condition