convergence analysis of inexact infeasible interior point algorithms for solving linear programming problems in this paper we present a convergence analysis for some inexact polynomial variants of the infeasible interior point algorithm of kojima megiddo and mizuno for this analysis we assume that the iterates are bounded the new variants allow the use of search directions that are calculated from the defining linear system with only moderate accuracy e g via the use of krylov subspace methods like cg or qmr furthermore some numerical results for the proposed methods are given

oscillation for solutions of nonlinear neutral differential equations with impulses abstract this paper is concerned with nonlinear neutral differential equations with impulses of the form some oscillation criteria for solutions of this equation are established an interesting example is also given which illustrates that impulses play an important role in giving rise to the oscillation of equations

necessary and sufficient conditions for oscillation of second order neutral differential equations consider the second order nonlinear neutral differential equation with delays e d2 dt2 y t py t q t f y t 0 for t 0 where q t f x are continuous functions q t 0 yf y 0 if y 0 and 0 0 0 when f y satisfies either the superlinear or sublinear conditions which include the special case f y y y 1 of 1 and 0 1 respectively we give necessary and sufficient conditions for the oscillation of all continuable solutions of e when p 0 in e these results reduce to the well known theorems of atkinson and belohorec in the special case when f y y y 1 1

oscillations of first order neutral delay differential equations abstract consider the neutral delay differential equation d dt y t py t qy t 0 t t 0 where q and are positive constants while p 1 0 for the case p 1 0 see ladas and sficas oscillations of neutral delay differential equations to appear the following results are then proved theorem 1 assume p and q 1 p 1 e then every solution of eq oscillates theorems 3 assume p 0 then every nonoscillatory solution y t of eq tends to zero as t theorem 4 assume p 0 then a necessary condition for all solutions of eq to oscillate is that theorem 5 assume p 0 and q 1 p 1 e then every solution of eq oscillates extensions of these results to equations with variable coefficients are also obtained

oscillation for first order nonlinear delay differential equations abstract almost sharp oscillation and nonoscillation criteria are obtained for the first order nonlinear delay differential equation x t p t j 1 m x t j j sign x t 1 0 t t 0 where j 1m j 1 some applications are given

a finite termination mehrotra type predictor corrector algorithm abstract mehrotra type predictor corrector algorithms are the backbone of most interior point methods based software packages salahi et al m salahi j peng t terlaky on mehrotra type predictor corrector algorithms technical report 2005 4 advanced optimization lab mcmaster university hamilton on canada http www cas mcmaster ca oplab publication in their recent works have shown some ill behaviors of mehrotra s original algorithm which motivated them to modify it in order to achieve the polynomial iteration complexity while preserving its practical efficiency in this paper we analyze the same algorithm from a different perspective and give a condition on the maximum feasible step size in the predictor step violation of which might lead to a very small or even zero step size in the corrector step if the maximum step size in the predictor step is above a certain threshold then we cut it to satisfy the derived condition this enables us to prove that the algorithm terminates finitely

on the oscillation of an n th order nonlinear neutral delay differential equation abstract the authors consider the n th order nonlinear neutral delay differential equation y t p t y g t n q t f y h t 0 where n 1 q t 0 and 1 they give sufficient conditions for solutions to either oscillate or converge to zero

qmr a quasi minimal residual method for non hermitian linear systems the biconjugate gradient bcg method is the natural generalization of the classical conjugate gradient algorithm for hermitian positive definite matrices to general non hermitian linear systems unfortunately the original bcg algorithm is susceptible to possible breakdowns and numerical instabilities in this paper we present a novel bcg like approach the quasi minimal residual qmr method which overcomes the problems of bcg an implementation of qmr based on a look ahead version of the nonsymmetric lanczos algorithm is proposed it is shown how bcg iterates can be recovered stably from the qmr process some further properties of the qmr approach are given and an error bound is presented finally numerical experiments are reported

necessary and sufficient conditions for oscillations of second order neutral equations consider the neutral delay differential equation d2dt2 y t py t qy t 0 1 where p q r and r we proved that eq 1 oscillates if and only if the characteristic equation 2 2pe qe 0 has no real roots

comment on the paper interval criteria for oscillation of second order nonlinear neutral differential equations comput math appl 46 5 6 2003 903 918

linearized oscillation of first order nonlinear neutral delay differential equations abstract in this paper we establish a equivalence of oscillation for the first order nonlinear neutral delay differential equation x t px t i 1 m q i f i x t i 0 and its corresponding linear equation x t px t i 1 m q i x t i 0 under a weaker condition on fi

on implementing mehrotra s predictor corrector interior point method for linear programming mehrotra tech report 90 03 department of industrial engineering and management sciences northwestern university evanston il 1990 recently described a predictor corrector variant of the primal dual interior point algorithm for linear programming this paper describes a full implementation of this algorithm with extensions for solving problems with free variables and problems with bounds on primal variables computational results on the netlib test set are given to show that this new method almost always improves the performance of the primal dual algorithm and that the improvement increases dramatically as the size and complexity of the problem increases a numerical instability in using schur complements to remove dense columns is identified and a numerical remedy is given

influence of dynamical noise on time series generated by nonlinear maps abstract we consider periodic and chaotic dynamics of discrete nonlinear maps in the presence of dynamical noise we show that dynamical noise corrupting dynamics of a nonlinear map may be considered as a measurement pseudonoise with the distribution determined by the jacobian of the map the formula for the distribution of the measurement pseudonoise for one dimensional quadratic maps has also been obtained in an explicit form we expect that our results apply to an arbitrary distribution of low level dynamical noise and hope that these results could help to find a universal method of discriminating dynamical from measurement noise

an implementation of karmarkar s algorithm for linear programming this paper describes the implementation of power series dual affine scaling variants of karmarkar s algorithm for linear programming based on a continuous version of karmarkar s algorithm two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested linear programs are expressed in an inequality form which allows for the inexact computation of the algorithm s direction of improvement resulting in a significant computational advantage implementation issues particular to this family of algorithms such as treatment of dense columns are discussed the code is tested on several standard linear programming problems and compares favorably with the simplex codeminos 4 0

asymptotic and oscillatory behavior of solutions of first order nonlinear neutral delay differential equations the authors consider the first order nonlinear neutral delay differential equation e y t p t y t q t y t 0 where p q and are continuous q t 0 0 0 and u u 0 if u 0 they give sufficient conditions for all nonoscillatory solutions of e to converge to zero as t two oscillation theorems for equation e are also proved

extreme value laws for dynamical systems under observational noise abstract in this paper we prove the existence of extreme value laws for dynamical systems perturbed by the instrument like error also called observational noise an orbit perturbed with observational noise mimics the behavior of an instrumentally recorded time series instrument characteristics defined as precision and accuracy act both by truncating and randomly displacing the real value of a measured observable here we analyze both these effects from a theoretical and a numerical point of view first we show that classical extreme value laws can be found for orbits of dynamical systems perturbed with observational noise then we present numerical experiments to support the theoretical findings and give an indication of the order of magnitude of the instrumental perturbations which cause relevant deviations from the extreme value laws observed in deterministic dynamical systems finally we show that the observational noise preserves the structure of the deterministic attractor this goes against the common assumption that random transformations cause the orbits asymptotically fill the ambient space with a loss of information about the fractal structure of the attractor

an asymptotical o sqrtnl iteration path following linear programming algorithm that uses wide neighborhoods path following linear programming lp algorithms generate a sequence of points within certain neighborhoods of a central path cal c which prevent iterates from prematurely getting too close to the boundary of the feasible region depending on the norm used these neighborhoods include cal n 2 beta cal n infty beta and cal n infty beta where beta in 0 1 and cal c subset cal n 2 beta subset cal n infty beta subset cal n infty beta quad mbox for each quad beta in 0 1 a paradox is that among all existing infeasible or feasible path following algorithms the theoretical iteration complexity o sqrt n l of small neighborhood cal n 2 algorithms is significantly better than the complexity o nl of wide neighborhood cal n infty algorithms in practice wide neighborhood algorithms outperform small neighborhood ones by a big margin here n is the number of lp variables and l is the lp data length in this paper we present an o n frac n 1 2n l iteration infeasible primal dual high order algorithm that uses wide neighborhoods note that this iteration bound is asymptotically o sqrt n l i e the best bound for small neighborhood algorithms as n increases

kamenev type oscillation criteria for even order neutral differential equations with deviating arguments abstract sufficient conditions are established for the oscillation of even order neutral differential equations of the form x t i 1 m p i t x i t n j 1 l q j t f j x j t 0 t t 0 where n 2 is even integer

oscillations of second order neutral functional differential equations abstract consider the second order neutral functional differential equation d 2 dt 2 x t n i 1 n i x t t i m j 1 j x t j 0 where 1 i i j and j i 1 2 n j 1 2 m are real numbers some new oscillation criteria are given for oscillation of e the results of this paper improve noticeably some known results

oscillation behavior of higher order neutral differential equations in this paper we establish sufficient conditions for the oscillation behavior of solutions of nth order neutral functional differential equations with distributed deviating arguments

discriminating additive from dynamical noise for chaotic time series we consider the dynamics of the h enon and ikeda maps in the presence of additive and dynamical noise we show that from the point of view of computations of some statistical quantities dynamical noise corrupting these deterministic systems can be considered effectively as an additive pseudonoise with the cauchy distribution in the case of the h enon and ikeda maps this effect occurs only for one variable of the system while the noise corrupting the second variable is still gaussian distributed independent of distribution of dynamical noise based on these results and using scaling properties of the correlation entropy we propose a simple method of discriminating additive from dynamical noise this approach is also useful for estimation of noise level for chaotic time series we show that the proposed method works well in a wide range of noise levels providing that one kind of noise predominates and we analyze the variable of the system for which the contamination follows cauchy like distribution in the presence of dynamical noise

postponing the choice of the barrier parameter in mehrotra type predictor corrector algorithms abstract recently salahi et al have considered a variant of mehrotra s celebrated predictor corrector algorithm by a numerical example they showed that this variant might make very small steps in order to keep the iterate in a certain neighborhood of the central path that itself implies the inefficiency of the algorithm this observation motivated them to incorporate a safeguard in their algorithmic scheme that gives a lower bound for the step size at each iteration and thus imply polynomial iteration complexity in this paper we propose a different approach that enables us to have control on the iterates our new approach is based on postponing the choice of the barrier parameter and it does not require any safeguard strategy to do so first we fix a step size in the corrector step then by solving a one dimensional optimization problem we calculate the barrier parameter finally using the calculated barrier parameter we make the next step it is proved for the feasible case that our new algorithm stops after at most o n 2 log n iterations without any safeguard strategy we further modified the proposed algorithm by slightly changing the newton system in the corrector step this variant enjoys an even better worst case iteration complexity bound i e o n log n superlinear convergence of both algorithms are established finally our numerical results demonstrate that a theoretically rigorous ipm may have the same or better computational efficiency than the ones enhanced by aggressive heuristics

complexity of predictor corrector algorithms for lcp based on a large neighborhood of the central path the predictor corrector approach for following the central path of monotone linear complementarity and linear programming problems is simple elegant and efficient although it has excellent theoretical properties when working in narrow neighborhoods of the central path its proved complexity assumes a frustratingly high value of o n1 5l iterations when based on an l infty neighborhood and several newton corrector steps per iteration this paper shows that by carefully specifying the line searches in each step the complexity assumes the value o nl as should be expected for a method based on this neighborhood

convergence of a class of inexact interior point algorithms for linear programs we present a convergence analysis for a class of inexact infeasible interior point methods for solving linear programs the main feature of inexact methods is that the linear systems defining the search direction at each interior point iteration need not be solved to high accuracy more precisely we allow that these linear systems are only solved to a moderate accuracy in the residual but no assumptions are made on the accuracy of the search direction in the search space in particular our analysis does not require that feasibility is maintained even if the initial iterate happened to be a feasible solution of the linear program we also present a few numerical examples to illustrate the effect of using inexact search directions on the number of interior point iterations

oscillatory behavior of second order half linear damped dynamic equations by refining the generalized riccati transformation technique we obtain new oscillation criteria for a class of second order half linear delay dynamic equations with damping on a time scale assumptions in our theorems are less restrictive these results complement and improve related contributions to the subject in particular the results obtained amend related results reported in the literature

existence for nonoscillatory solutions of second order nonlinear differential equations abstract in this paper the existence of nonoscillatory solutions of the second order nonlinear neutral differential equation r t x t p t x t i 1 m q i t f i x t i 0 t t 0 where m 1 is an integer 0 i 0 r p q i c t 0 r f i c r r i 1 2 m are studied some new sufficient conditions for the existence of a nonoscillatory solution of above equation are obtained for general p t and q i t i 1 2 m which means that we allow oscillatory p t and q i t i 1 2 m in particular our results improve essentially and extend some known results in the recent references

some remarks on oscillation of second order neutral differential equations we study oscillatory behavior of a class of nonlinear second order neutral differential equations a new criterion is established that amends related results reported in the literature

oscillation and existence of positive solutions in a class of higher order neutral equations abstract consider the higher order neutral differential equation x t x t n q t x t 0 t t 0 with q t continuous 0 0 and n odd we establish several new sufficient conditions for the oscillation of all solutions and the existence of a positive solution by an associated ordinary differential equation some of these conditions are sharp and improve the known results in the literature which include the newest one by 8

error covariance matrix estimation of noisy and dynamically coupled time series we estimate the covariance matrix of the errors in several dynamically coupled time series corrupted by measurement errors we say that several scalar time series are dynamically coupled if they record the values of measurements of the state variables of the same smooth dynamical system the estimation of the covariance matrix of the errors is made using a noise reduction algorithm that efficiently exploits the information contained jointly in the dynamically coupled noisy time series the method is particularly powerful for short length time series with high uncertainties

a self correcting version of karmarkar s algorithm a relaxed version of karmarkar s algorithm is developed that does not require the direction of movement to be in the null space of the constraint matrix the algorithm is proved to have the same rate of convergence as karmarkar s algorithm conditions are also given guaranteeing that the approach suggested by karmarkar for transforming an inequality form linear program into the form required by his algorithm is well defined

new nonoscillation criteria for delay differential equations abstract this paper is concerned with the nonoscillation of first order delay differential equations of the form x t p t x t 0 t t 0 where p c t 0 r r 0 t is nondecreasing t t for t t 0 and lim t t new nonoscillation conditions are obtained these conditions concern the case when the well known nonoscillation condition t t p s ds 1 e is not satisfied

on finding a vertex solution using interior point methods abstract an approach is proposed to generate a vertex solution while using a primal dual interior point method to solve linear programs a controlled random perturbation is made to the cost vector a method to identify the active constraints at the vertex to which the solutions are converging is given this basic method is further refined to save computational effort the proposed approach is tested by using a variation of the primal dual interior point method our method is developed by taking a predictor corrector approach in practice this method takes considerably fewer iterations to solve linear programs than methods described by choi monma and shanno lustig marsten and shanno and domich boggs donaldson and witzgall computational results on problems from the netlib test set are reported to test our approach for finding vertex solutions these results show that one perturbation is enough to force the solutions to converge to a vertex the results indicate that the proposed approach is insensitive to the number of degenerate variables the results also indicate that the effort required to generate a vertex solution is comparable to that required to solve the problem using an interior point method

oscillation by impulses for a second order delay differential equation we consider a certain second order nonlinear delay differential equation and prove that the all solutions oscillate when proper impulse controls are imposed an example is given

multifractality and randomness in the unstable plastic flow near the lower strain rate boundary of instability the unstable plastic flow of an almg alloy associated with the portevin le chatelier effect was studied near the lower strain rate boundary of instability using multifractal analysis self similarity of deformation curves indicating long range time correlations of stress serrations was detected within the strain rate range where serrations are commonly ascribed to the occurrence of uncorrelated deformation bands the deformation curves display a wide range of shapes that are characterized by different groupings of serrations multifractal analysis provides a method to quantify the observed complexity and compare it to known portevin le chatelier effect regimes the measurement noise effect on the multifractal spectra determined from experimental data was mimicked by superposing multifractal cantor sets with random noise such tests using standard multifractal data sets justify the separation of self similar and random components of the serrated deformation curves furthermore these results shed light on the general problem of the effect of experimental noise on the apparent multifractal properties of physical fractals

oscillatory behavior of higher order nonlinear neutral forced differential equations with oscillating coefficients in this paper the higher order nonlinear neutral forced differential equations of the form x t p t x t t n i 1mq i t f i x s i t s t t t 0 where n m n n 2 and m 1 are studied a new necessary and sufficient theorem for the oscillation of bounded solutions and a sufficient criterion for the existence of bounded positive solutions of the above equations are obtained for general p t and s t in particular our results improve some known results

on oscillation of second order neutral type delay differential equations oscillation criteria are obtained by using the so called h method for the second order neutral type delay differential equations of the form r t j x t z t q t f x s t 0 t t 0 where z t x t p t x t t r p q t s c t 0 r and f email protected c r r the results of the paper contains several results obtained previously as special cases furthermore we are also able to fix an error in a recent paper related to the oscillation of second order nonneutral delay differential equations

oscillation for a second order neutral differential equation with impulses we consider a certain type of second order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations called impulses as a matter of fact some particular non impulsive cases of the system are oscillatory already thus we are interested in finding adequate impulse controls under which our system remains oscillatory

oscillation of second order nonlinear neutral differential equations consider the second order nonlinear neutral delay differential equation r t x t p t x email protected a f t x email protected 0 e where t and s are nonnegative constants and a is a quotient of positive odd integers some new oscillatory criteria for eq e are established several examples which dwell upon the importance of our results are also illustrated

on mehrotra type predictor corrector algorithms in this paper we discuss the polynomiality of a feasible version of mehrotra s predictor corrector algorithm whose variants have been widely used in several interior point method ipm based optimization packages a numerical example is given that shows that the adaptive choice of centering parameter and correction terms in this algorithm may lead to small steps being taken in order to keep the iterates in a large neighborhood of the central path which is important for proving polynomial complexity properties of this method motivated by this example we introduce a safeguard in mehrotra s algorithm that keeps the iterates in the prescribed neighborhood and allows us to obtain a positive lower bound on the step size this safeguard strategy is also used when the affine scaling direction performs poorly we prove that the safeguarded algorithm will terminate after at most cal o n 2 rm log x 0 ts 0 epsilon iterations by modestly modifying the corrector direction we reduce the iteration complexity to cal o n rm log x 0 ts 0 epsilon to ensure fast asymptotic convergence of the algorithm we changed mehrotra s updating scheme of the centering parameter slightly while keeping the safeguard the new algorithms have the same order of iteration complexity as the safeguarded algorithms but enjoy superlinear convergence as well numerical results using the mcipm and lipsol software packages are reported

the mizuno todd ye algorithm in a larger neighborhood of the central path the mizuno todd ye predictor corrector method based on two neighborhoods d a d a of the central path of a monotone homogeneous linear complementarity problem is analyzed where d a is composed of all feasible points with d proximity to the central path less than or equal to a the largest allowable value for a is 1 76 for a specific choice of a and a a lower bound of vn ffiffiffi n p is obtained for the stepsize along the affine scaling direction where vn has an asymptotic value greater than 1 08 for n p 400 it is shown that vn 1 05 the algorithm has o ffiffiffi n p l iteration

oscillation and asymptotic analysis on a new generalized emden fowler equation abstract in this work we analyze the new generalized emden fowler equation with neutral type delays r t z t 1 z t q t x t 1 x t 0 where z t x t p t x t 0 by use of averaging technique and specific analytical skills some easily accessible oscillation and asymptotic criteria are established which have extended the results in the cited literature

oscillation of impulsive neutral delay differential equations abstract in this paper effective sufficient conditions for the oscillation of all solutions of impulsive neutral delay differential equations of the form x t p t x t q t x t sgn x t 0 t t 0 x t k b k x t k k 1 2 are established our results reveal the fact that the oscillatory properties of all solutions of eqs and may be caused by the impulsive perturbations though the corresponding neutral delay differential equation without impulses i e eq admits a nonoscillatory solution it is also seen that the oscillatory behavior of all solutions of eq can be inherited by eqs and under certain impulsive perturbations some examples are also given to illustrate the applicability of the results obtained

polynomial time second order mehrotra type predictor corrector algorithms salahi et al m salahi j peng t terlaky on mehrtora type predictor corrector algorithms technical report 2005 4 advanced optimization lab department of computing and software mcmaster university http www cas mcmaster ca oplab publication siam journal on optimization submitted for publication give a numerical example showing that mehrotra s original predictor corrector algorithm which is the basis of interior point methods software packages may be very inefficient in practice this motivated salahi et al to come up with a safeguarded algorithm that enjoys a polynomial iteration complexity and is efficient in practice here we discuss a variation of mehrotra s second order predictor corrector algorithm s mehrotra on the implementation of a primal dual interior point method siam journal on optimization 2 1992 575 601 and use the example of salahi et al to show that the algorithm may have to take very small steps in order to remain in a certain neighborhood of the central path and subsequently needs excessively large number of iterations to stop we then introduce a safeguard that guarantees a lower bound for the maximum step size in the corrector step of the algorithm and subsequently a polynomial number of iterations a second modification of algorithm is proposed which enjoys even a better iteration complexity some limited encouraging computational results are reported

oscillatory behaviour of higher order neutral type nonlinear forced differential equation with oscillating coefficients abstract oscillation criteria are given for higher order neutral type nonlinear forced differential equation with oscillating coefficients of the form y t p t y t n i 1 m q i t f i y i t s t

a qmr based interior point algorithm for solving linear programs a new approach for the implementation of interior point methods for solving linear programs is proposed its main feature is the iterative solution of the symmetric but highly indefinite 2 2 block systems of linear equations that arise within the interior point algorithm these linear systems are solved by a symmetric variant of the quasi minimal residual qmr algorithm which is an iterative solver for general linear systems the symmetric qmr algorithm can be combined with indefinite preconditioners which is crucial for the efficient solution of highly indefinite linear systems yet it still fully exploits the symmetry of the linear systems to be solved to support the use of the symmetric qmr iteration a novel stable reduction of the original unsymmetric 3 3 block systems to symmetric 2 2 block systems is introduced and a measure for a low relative accuracy for the solution of these linear systems within the interior point algorithm is proposed some indefinite preconditioners are discussed finally we report results of a few preliminary numerical experiments to illustrate the features of the new approach

solvability and iterative algorithms for a higher order nonlinear neutral delay differential equation the paper is concerned with the higher order nonlinear neutral delay differential equation r t x t p t x email protected m n m 1 n m 1ft email protected 1 t x s l t g t t t 0 using the banach fixed point theorem we establish five existence results of uncountably many bounded nonoscillatory solutions for the above equation construct five mann iterative sequences with mixed errors for approximating these nonoscillatory solutions and discuss five error estimates between the approximate solutions and these nonoscillatory solutions to dwell the importance and applications of our results five nontrivial examples are constructed

a oscillation theorem for a class of even order neutral differential equations abstract the even order neutral differential equation 1 d n dt n x t h t x t f t x g t 0 is considered under the following conditions n 2 is even 0 h c r g c t 0 lim t g t f c t 0 r uf t u 0 for t u t 0 r and f t u is nondecreasing in u r for each fixed t t 0 it is shown that 1 is oscillatory if and only if the certain non neutral differential equation is oscillatory for the case where 0 h t h t

corrigendum to necessary and sufficient conditions for oscillation of second order neutral differential equations j math anal appl 252 2000 342 352

solving symmetric indefinite systems in an interior point method for linear programming we describe an implementation of a primal dual path following method for linear programming that solves symmetric indefinite augmented systems directly by bunch parlett factorization rather than reducing these systems to the positive definite normal equations that are solved by cholesky factorization in many existing implementations the augmented system approach is seen to avoid difficulties of numerical instability and inefficiency associated with free variables and with dense columns in the normal equations approach solving the indefinite systems does incur an extra overhead whose median is about 40 in our tests but the augmented system approach proves to be faster for a minority of cases in which the normal equations have relatively dense cholesky factors a detailed analysis shows that the augmented system factorization is reliable over a fairly large range of the parameter settings that control the tradeoff between sparsity and numerical stability

the asymptotic and oscillatory behavior of the solutions of higher order neutral equations abstract consider the higher order neutral differential equation y t i 1 n1 p i y t i j 1 n2 r j y t j n s 1 n3 q s y t 0 we study the asymptotic behavior of solutions of eq 1 and we obtain several sufficient conditions for the oscillation of solutions of eq 1 this paper generalizes all results of ladas and sficas 1

linearized oscillations for even order neutral differential equations abstract we are concerned with the oscillation of all bounded solutions of some even order linear neutral delay differential equations we establish a comparison theorem and a linearized oscillation result and we prove the existence of a bounded positive solution

convergence conditions and krylov subspace based corrections for primal dual interior point method we present convergence conditions for a generic primal dual interior point algorithm with multiple corrector directions the corrector directions can be generated by any approach the search direction is obtained by combining predictor and corrector directions through a small linear program we also propose a new approach to generate corrector directions this approach generates directions using information from an appropriately defined krylov subspace we propose efficient implementation strategies for our approach that follow the analysis of this paper numerical experiments illustrating the features of the proposed approach and its practical usefulness are reported

asymptotic and oscillatory behavior of solutions of nonlinear neutral delay equations of arbitrary order abstract the authors obtain results on the oscillatory and asymptotic behavior of solutions of the nonlinear neutral delay differential equation y t p t y g t n f t y h t 0 where n 1 1 and uf t u 0 for u 0 several known results of this type are included as special cases examples illustrating their results are included

oscillation of second order nonlinear neutral dynamic equations on time scales with distributed deviating arguments this article is concerned with oscillation of second order neutral dynamic equations with distributed deviating arguments of the form r t y t p t y t t d c email protected c df t y q t x email protected 0 where c 0 is a ratio of odd positive integers with r t and p t real valued rd continuous positive functions defined on t we establish some new oscillation criteria and give sufficient conditions to insure that all solutions of nonlinear neutral dynamic equation are oscillatory on a time scale t

a new infinity norm path following algorithm for linear programming we devise a new primal dual path following algorithm for linear programming that is based entirely on an infinity norm centering measure the algorithm makes reductions in a path parameter mu each of which is followed by a sequence of centering steps the algorithm has similarities with both long step path following and predictor corrector methods we also consider a modified version of the algorithm that uses partial updating of the projection equations the analysis of the modified algorithm has some interesting differences compared with previously devised partial updating methods in particular partial updating obtains a factor of sqrt n complexity reduction even though the permissible relative error in the approximate scaling factors is extremely small only o 1 sqrt n

computational experience with a primal dual interior point method for linear programming abstract a new comprehensive implementation of a primal dual algorithm for linear programming is described it allows for easy handling of simple bounds on the primal variables and incorporates free variables which have not previously been included in a primal dual implementation we discuss in detail a variety of computational issues concerning the primal dual implementation and barrier methods for linear programming in general we show that in a certain way lustig s method for obtaining feasibility is equivalent to newton s method this demonstrates that the method is in some sense the natural way to reduce infeasibility the role of the barrier parameter in computational practice is studied in detail numerical results are given for the entire expanded netlib test set for the basic algorithm and its variants as well as version 5 3 of minos

oscillation and existence of positive solutions for odd order neutral equations with integrally small coefficients abstract consider the odd order neutral differential equation formula we establish several new sufficient conditions for the oscillation of all solutions and the existence of a positive solution when p t 1 is allowed to oscillate and the usual divergent condition q s ds is not satisfied these conditions are almost sharp and improve some known results in the literature some examples are given to demonstrate the advantage of our results

oscillation of second order nonlinear neutral delay dynamic equations on time scales in this paper some sufficient conditions for oscillation of the second order nonlinear neutral delay dynamic equation r t y t p t y t f t y t 0 on a time scale t are established here 1 is an odd positive integer with r t and p t are rd continuous functions defined on t our results as a special case when t r and t n involve and improve some well known oscillation results for second order neutral delay differential and difference equations when t hn and t qn t t qk k n q 1 i e for generalized neutral delay difference and q neutral delay difference equations our results are essentially new and also can be applied on different types of time scales e g t n2 t2 t n and t tn tn n n0 where tn is the set of harmonic numbers some examples illustrating our main results are given

oscillation of second order nonlinear neutral differential equations abstract in this paper some sufficient conditions for oscillation and nonoscillation are obtained for the second order nonlinear neutral differential equation x t p t x t q t f x t 0 t 0 where 0 p t 1 q t 0 0

oscillation criteria for nth order nonlinear neutral differential equations abstract sufficient conditions are established for the oscillation of nth order neutral differential equations of the form r t x t x t 1 p t x t n 1 q t f x t 0 t t 0 where n 2 is even integer 1 p q c t 0 r f c r r the results obtained extend some of the known results