convergence of a halpern type iteration algorithm for a class of pseudo contractive mappings abstract let e be a real reflexive banach space with uniformly g teaux differentiable norm let k be a nonempty bounded closed and convex subset of e let t k k be a strictly pseudo contractive map and let l 0 denote its lipschitz constant assume f t x k t x x 0 and let z f t fix 0 1 and let be such that l 0 1 define s n x 1 n x n t x x k where n 0 1 and lim n 0 let n be a real sequence in 0 1 which satisfies the following conditions c1 lim n 0 c2 n for arbitrary x 0 u k define a sequence x n k by x n 1 n u 1 n s n x n then x n converges strongly to a fixed point of t

the lagrangian relaxation method for solving integer programming problems this article originally appeared in management science january 1981 volume 27 number 1 pp 1 18 published by the institute of management sciences one of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints dualizing the side constraints produces a lagrangian problem that is easy to solve and whose optimal value is a lower bound for minimization problems on the optimal value of the original problem the lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm this approach has led to dramatically improved algorithms for a number of important problems in the areas of routing location scheduling assignment and set covering this paper is a review of lagrangian relaxation based on what has been learned in the last decade

a new iterative algorithm for common solutions of a finite family of accretive operators abstract the purpose in this paper is to prove a theorem of strong convergence to a common solution for a finite family of accretive operators in a strictly convex banach space by means of a new iterative algorithm which is a generalization and extension of the results of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 and zegeye and shahzad h zegeye n shahzad strong convergence theorems for a common zero of a finite family of m accretive mappings nonlinear anal 66 2007 1161 1169 further using the result the theorem of strong convergence to a common fixed point is discussed for a finite family of pseudocontractive mappings under certain conditions

the complex cepstrum of higher order cumulants and nonminimum phase system identification a computationally efficient identification procedure is proposed for a nongaussian white noise driven linear time invariant nonminimum phase system the method is based on the idea of computing the complex cepstrum of higher order cumulants of the system output in particular the differential cepstrum parameters of the nonminimum phase impulse response are estimated directly from higher order cumulants by least squares solution or two dimensional fft operations the method reconstructs the minimum phase and maximum phase impulse response components separately it is flexible enough to be applied on autoregressive ar moving average ma or arma system without a priori knowledge of the type of the system benchmark simulation examples demonstrate the effectiveness of the method even with short length data records

a bound for the symmetric travelling salesman problem through matroid formulation abstract a new bound for the symmetric traveling salesman problem is proposed using a matroid theoretic formulation of the problem the resulting bound is shown to present a link between the well studied 1 tree and 2 matching bounds its potential is investigated

an exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts this paper presents a new exact algorithm for the capacitated vehicle routing problem cvrp based on the set partitioning formulation with additional cuts that correspond to capacity and clique inequalities the exact algorithm uses a bounding procedure that finds a near optimal dual solution of the lp relaxation of the resulting mathematical formulation by combining three dual ascent heuristics the first dual heuristic is based on the q route relaxation of the set partitioning formulation of the cvrp the second one combines lagrangean relaxation pricing and cut generation the third attempts to close the duality gap left by the first two procedures using a classical pricing and cut generation technique the final dual solution is used to generate a reduced problem containing only the routes whose reduced costs are smaller than the gap between an upper bound and the lower bound achieved the resulting problem is solved by an integer programming solver computational results over the main instances from the literature show the effectiveness of the proposed algorithm

the traveling salesman problem an overview of exact and approximate algorithms in this paper some of the main known algorithms for the traveling salesman problem are surveyed the paper is organized as follows 1 definition 2 applications 3 complexity analysis 4 exact algorithms 5 heuristic algorithms 6 conclusion

convergence theorems for common fixed points for finite families of nonexpansive mappings in reflexive banach spaces let e be a real reflexive banach space with a uniformly g teaux differentiable norm let k be a nonempty closed convex subset of e suppose that every nonempty closed convex bounded subset of k has the fixed point property for nonexpansive mappings let t1 t2 tn be a family of nonexpansive self mappings of k with f i 1nfix ti 0 f fix tntn 1 t1 fix t1tn t2 fix tn 1tn 2 t1tn let n be a sequence in 0 1 satisfying the following conditions c1 lim n 0 c2 n for a fixed 0 1 define sn k k by snx 1 x tnx x k where tn tnmodn for an arbitrary fixed u x0 k let b x k tntn 1 t1x x 1 u for some 1 be bounded and let the sequence xn be defined iteratively by xn 1 n 1u 1 n 1 sn 1xn for n 0 assume that limn tnxn tn 1xn 0 then xn converges strongly to a common fixed point of the family t1 t2 tn this convergence theorem is also proved for non self maps

a parallel branch and bound algorithm for solving large asymmetric traveling salesman problems a parallel branch and bound algorithm that solves the asymmetric traveling salesman problem to optimality is described the algorithm uses an assignment problem based lower bounding technique subtour elimination branching rules and a subtour patching algorithm as an upper bounding procedure the algorithm is organized around a data flow framework for parallel branch and bound the algorithm begins by converting the cost matrix to a sparser version in such a fashion as to retain the optimality of the final solution computational results are presented for three different classes of problem instances 1 matrix elements drawn from a uniform distribution of integers for instances of size 250 to 10 000 cities 2 instances of size 250 to 1000 cities that concentrate small elements in the upper left portion of the cost matrix and 3 instances of size 300 to 3000 cities that are designed to confound neighborhood search heuristics

strong convergence theorems for uniformly continuous pseudocontractive maps abstract let k be a nonempty closed convex subset of a real banach space e and let t k k be a uniformly continuous pseudocontraction fix any u k let x n be defined by the iterative process x 0 k x n 1 n n t x n 1 n x n 1 n u let denote the modulus of continuity of t with pseudo inverse if t t 0 t 1 and x n are bounded then under some mild conditions on the sequences n n and n n the strong convergence of x n to a fixed point of t is proved in the special case where t is lipschitz it is shown that the boundedness assumptions on t t 0 t 1 and x n can be dispensed with

a new sufficient condition for the strong convergence of halpern type iterations abstract the aim of this work is to give a new sufficient condition of the strong convergence of the halpern type iteration for a non expansive self mapping defined on a banach space with a uniformly g teaux differentiable norm several examples satisfying our condition are presented our results not only remove the restriction of the space with the fixed point property for non expansive self mappings but also get rid of the dependence on the convergence of the implicit anchor like continuous path z t in the proof

an additive bounding procedure for combinatorial optimization problems we know that the effectiveness of the branch and bound algorithms proposed for the solution of combinatorial optimization problems greatly depends on the tightness of the available bounds in this paper we consider optimization problems with a linear objective function we propose an additive approach for computing lower bounds that yields an increasing sequence of values an application to the traveling salesman problem with precedence constraints is presented to exemplify the technique

hybrid optimization methods for time dependent sequencing problems abstract in this paper we introduce novel optimization methods for sequencing problems in which the setup times between a pair of tasks depend on the relative position of the tasks in the ordering our proposed methods rely on a hybrid approach where a constraint programming model is enhanced with two distinct relaxations one discrete relaxation based on multivalued decision diagrams and one continuous relaxation based on linear programming both relaxations are used to generate bounds and enhance constraint propagation experiments conducted on three variants of the time dependent traveling salesman problem indicate that our techniques substantially outperform general purpose methods such as mixed integer linear programming and constraint programming models

halpern s iteration for bregman strongly nonexpansive mappings in reflexive banach spaces we investigate strong convergence for bregman strongly nonexpansive mappings by halpern s iteration in the framework of reflexive banach spaces using the obtained result convergence for a family of bregman strongly nonexpansive mappings is also discussed as applications we apply our main result to problems of finding zeros of maximal monotone operators and equilibrium problems in reflexive banach spaces

subspace based channel shortening for the blind separation of convolutive mixtures a novel subspace based channel shortening procedure is proposed based on the structure of the delayed autocorrelation matrices of the observation process this purely second order approach applies to overdetermined multiple input multiple output mimo channels with independent white sources the channel may be sparse and its length is assumed to be unknown through successive deflations the problem can be transformed into an instantaneous blind source separation bss problem which is simpler to solve using for example independent component analysis ica techniques the algorithm is computationally fast although it requires large input datasets such data can be acquired either through large numbers of sensors or by using increased data sampling rate when not enough data are available the method can still be used for reducing the channel length thus simplifying the problem for subsequent treatment

a hybrid algorithm for pseudo contractive mappings abstract in this paper we suggest and analyze a hybrid algorithm for pseudo contractive mappings in hilbert spaces further we prove the strong convergence of the proposed iterative algorithm for lipschitz pseudo contractive mappings in hilbert spaces

strong convergence of krasnoselskii and mann s type sequences for one parameter nonexpansive semigroups without bochner integrals abstract in this paper we prove krasnoselskii and mann s type convergence theorems for nonexpansive semigroups without using bochner integral and without assuming the strict convexity of banach spaces one of our main results is the following let c be a compact convex subset of a banach space e and let t t t 0 be a one parameter strongly continuous semigroup of nonexpansive mappings on c let t n be a sequence in 0 satisfying lim inf n t n lim sup n t n and lim n t n 1 t n 0 let 0 1 define a sequence x n in c by x 1 c and x n 1 t t n x n 1 x n for n n then x n converges strongly to a common fixed point of t t t 0

an efficient genetic algorithm for the traveling salesman problem with precedence constraints abstract the traveling salesman problem with precedence constraints tsppc is one of the most difficult combinatorial optimization problems in this paper an efficient genetic algorithm ga to solve the tsppc is presented the key concept of the proposed ga is a topological sort ts which is defined as an ordering of vertices in a directed graph also a new crossover operation is developed for the proposed ga the results of numerical experiments show that the proposed ga produces an optimal solution and shows superior performance compared to the traditional algorithms

a branch and bound algorithm for the symmetric traveling salesman problem based on the 1 tree relaxation abstract in 1970 held and karp introduced the lagrangean approach to the symmetric traveling salesman problem we use this 1 tree relaxation in a new branch and bound algorithm it differs from other algorithms not only in the branching scheme but also in the ascent method to calculate the 1 tree bounds urthermore we determine heuristic solutions throughout the computations to provide upperbounds we present computational results for both a depth first and a breadth first version of our algorithm on the average our results on a number of euclidean problems from the literature are obtained in about 60 less 1 trees than the best known algorithm based on the 1 tree relaxation for random table problems up to 100 cities the average results are also satisfactory

optimal training sequence for mimo wireless systems in colored environments in this paper we design the training signal for a multi input multi output mimo communication system in a colored medium we assume that the known channel covariance matrix cm is a kronecker product of a transmit channel cm and a receive channel cm similarly the cm of the additive gaussian noise is modeled by a kronecker product of a temporal cm and a spatial cm we maximize the differential entropy gained by receiver for a limited energy budget for training at the transmitter using singular value decomposition of the involved cms we turn this problem into a convex optimization problem we prove that the left and right singular vectors of the optimal training matrix are eigenvectors of the channel transmit cm and the noise temporal cm in general case this problem can be solved numerically using efficient methods the impact of the optimal training is more significant in environments with larger eigenvalue spread the expression of the optimal solution is interesting for some specific cases for uncorrelated receive channel the optimal training looks like water filling i e more training power must be invested on the directions which have more impact for high signal to noise ratios snrs any orthogonal training is optimal this means that if large amount of energy is available it must be invested uniformly in all directions in low snr scenarios where low amount of energy is available for channel training all the energy must be allocated to the best mode of channel which has the highest ratio of the received channel variance to the received noise power

a column generation approach to the multiple depot vehicle scheduling problem we give a new formulation to the multiple depot vehicle scheduling problem as a set partitioning problem with side constraints whose continuous relaxation is amenable to be solved by column generation we show that the continuous relaxation of the set partitioning formulation provides a much tighter lower bound than the additive bound procedure previously applied to this problem we also establish that the additive bound technique cannot provide tighter bounds than those obtained by lagrangian decomposition in the framework in which it has been used so far computational results that illustrate the robustness of the combined set partitioning column generation approach are reported for problems four to five times larger than the largest problems that have been exactly solved in the literature finally we show that the gap associated with the additive bound based on the assignment and shortest path relaxations can be arbitrarily bad in the general case and as bad as 50 in the symmetric case

blind equalization using a tricepstrum based algorithm an adaptive blind equalization method is introduced for nonminimum phase communication channels the method estimates the inverse channel impulse response by using the complex cepstrum of the fourth order cumulants tricepstrum of the synchronously sampled received signal as such the proposed adaptive method depends only on the statistics of the received sequence and is capable of reconstructing separately both the minimum and maximum phase response of the channel it is demonstrated by means of extensive simulations that the proposed tricepstrum based equalization scheme performs well and outperforms other existing blind equalizers at the expense of higher computational complexity

embedding learning capability in lagrangean relaxation an application to the travelling salesman problem abstract this paper presents an effective procedure that finds lower bounds for the travelling salesman problem based on the 1 tree using a learning based lagrangian relaxation technique the procedure can dynamically alter its step size depending upon its previous iterations along with having the capability of expansion contraction the procedure performs a learning process in which lagrange multipliers are influenced by a weighted cost function of their neighbouring nodes in analogy with simulated annealing paradigm here a learning process is equivalent to escaping local optimality via exploiting the structure of the problem computational results conducted on euclidean benchmarks from the tsplib library show that the procedure is very effective

a restricted lagrangean approach to the traveling salesman problem we describe an algorithm for the asymmetric traveling salesman problem tsp using a new restricted lagrangean relaxation based on the assignment problem ap the lagrange multipliers are constrained so as to guarantee the continued optimality of the initial ap solution thus eliminating the need for repeatedly solving ap in the process of computing multipliers we give several polynomially bounded procedures for generating valid inequalities and taking them into the lagrangean function with a positive multiplier without violating the constraints so as to strengthen the current lower bound upper bounds are generated by a fast tour building heuristic when the bound strengthening techniques are exhausted without matching the upper with the lower bound we branch by using two different rules according to the situation the usual subtour breaking disjunction and a new disjunction based on conditional bounds we discuss computational experience on 120 randomly generated asymmetric tsp s with up to 325 cities the maximum time used for any single problem being 82 seconds this is a considerable improvement upon earlier methods though the algorithm discussed here is for the asymmetric tsp the approach can be adapted to the symmetric tsp by using the 2 matching problem instead of ap

strong convergence of an iterative method for nonexpansive mappings with new control conditions abstract the purpose of this paper is to study the convergence problem of an iterative method for nonexpansive mappings in banach spaces under some new control conditions on parameters

cross spectrum based blind channel identification a novel cross correlation based framework is proposed for the problem of blind equalization in communications we assume that we have access to two observations obtained either by sampling at the symbol rate the outputs of two sensors or by oversampling by a factor of two the output of a single sensor in either case the two observations correspond to the outputs of two channels excited by the same input the channels are estimated using the theory of signal reconstruction from phase only the phase used is the phase of the cross spectrum of the observations filtered through their minimum phase equivalent filters we provide an analytical study of the propagation of noise effects in the phase estimate comparisons with existing methods indicate that the proposed approach is robust to noise and at low signal to noise ratio snr leads to significantly smaller channel estimation errors besides robustness to noise the proposed method does not require knowledge of channel lengths which are determined via an iterative procedure

the symmetric clustered traveling salesman problem abstract the clustered traveling salesman problem is the well known standard problem with additional constraints the cities are divided into groups and each group of cities cluster must be visited contiguously we describe an extensive adaptation of an existing traveling salesman algorithm based on the 1 tree relaxation in the lagrangean approach a new multiplier is introduced to improve the lower bounds furthermore we describe a heuristic to find satisfactory upper bounds and discuss the elimination of nonoptimal edges the computational results are satisfying and include random euclidean problems up to 150 cities

a branch and bound algorithm for the capacitated vehicle routing problem on directed graphs we consider the asymmetric capacitated vehicle routing problem cvrp a particular case of the standard asymmetric vehicle routing problem in which only the vehicle capacity constraints are imposed cvrp is known to be np hard and finds practical applications in distribution and scheduling we describe two new bounding procedures for cvrp based on the so called additive approach each procedure computes a sequence of nondecreasing lower bounds obtained by solving different relaxations of cvrp effective implementations of the procedures are also outlined which considerably reduce the computational effort the two procedures are combined into an overall bounding algorithm a branch and bound exact algorithm is then proposed whose performance is enhanced by means of reduction procedures dominance criteria and feasibility checks extensive computational results on both real world and random test problems are presented showing that the proposed approach favorably compares with previous algorithms from the literature

a useful transform of standard input data for a classical np complete problem abstract the archetypal symmetric travelling salesman problem can be seen in a new and interesting way by using first a standard preparatory phase of input data and then by applying a transform from the set d of distances among cities and the set b of loss of optimality the specific form of d b transform is introduced and discussed in order to show in realistic terms the interest of the approach proposed a class of diffusive heuristic procedures operating from b is defined an example of solution by an algorithm included in this class is completely worked out an outline of computational tests done on the same algorithm is also given

iterative approximation of fixed points of nonexpansive mappings let k be a nonempty closed convex subset of a real banach space e which has a uniformly g teaux differentiable norm and t k k be a nonexpansive mapping with f t x k tx x for a fixed 0 1 define s k k by sx 1 x tx x k assume that zt converges strongly to a fixed point z of t as t 0 where zt is the unique element of k which satisfies zt tu 1 t tzt for arbitrary u k let n be a real sequence in 0 1 which satisfies the following conditions c1 lim n 0 c2 n for arbitrary x0 k let the sequence xn be defined iteratively by xn 1 nu 1 n sxn then xn converges strongly to a fixed point of t

using logical surrogate information in lagrangean relaxation an application to symmetric traveling salesman problems abstract the traveling salesman problem tsp is a classical combinatorial optimization problem which has been intensively studied the lagrangean relaxation was first applied to the tsp in 1970 the lagrangean relaxation limit approximates what is known today as held and karp hk bound a very good bound less than 1 from optimal for a large class of symmetric instances it became a reference bound for new heuristics mainly for the very large scale instances where the use of exact methods is prohibitive a known problem for the lagrangean relaxation application is the definition of a convenient step size control in subgradient like methods even preserving theoretical convergence properties a wrong defined control can affect the performance and increase computational times we show in this work how to accelerate a classical subgradient method while conserving good approximations to the hk bounds the surrogate and lagrangean relaxations are combined using the local information of the relaxed constraints it results in a one dimensional search that corrects the possibly wrong step size and is independent of the used step size control comparing with the ordinary subgradient method and beginning with the same initial multiplier the computational times are almost twice as fast for medium instances and greatly improved for some large scale tsplib instances

the viscosity approximation process for quasi nonexpansive mappings in hilbert spaces in this paper we discuss the strong convergence of the viscosity approximation method in hilbert spaces relatively to the computation of fixed points of operators in the wide class of quasi nonexpansive mappings our convergence results improve previously known ones obtained for the class of nonexpansive mappings

fourth order spatial correlation coefficient across the uplink receiver s spatial aperture analytically derived in closed form this paper is first in the open literature to the authors best knowledge on wireless channel fading to derive the uplink received signal s fourth order spatial correlation coefficient function across a receiving sensor array s aperture this derivation is mathematically rigorous and is based on idealized geometric relationships among the mobile transmitter the base station s receiving antennas and the scatterers of the channel the scatterers spatial locations are modeled as poisson distributed with a gaussian intensity over a two dimensional space this scatterer model has previously been empirically verified to produce faithful expressions for the second order spatial correlation coefficient the final formula is in closed form explicit in terms of the simple geometric model s few independent parameters

nonoptimal edges for the symmetric traveling salesman problem for the symmetric traveling salesman problem we identify a set of undirected edges that can be eliminated while still retaining at least one optimal solution of the problem the simple identification rules are based on the fact that a solution can be optimal only if it is 2 optimal the rules are less stringent than those formulated for nonoptimal arcs directed applied to the symmetric case so in general they identify more nonoptimal edges application of the theory in a 1 tree based traveling salesman algorithm roughly halves the average computation time for euclidean problems we indicate to what extent the theorems presented here can be adapted for variants of the traveling salesman problem

an optimal solution method for large scale multiple traveling salesmen problems we develop an efficient branch and bound based method for solving the multiple traveling salesman problem and develop lower bounds through a lagrangean relaxation that requires computing a degree constrained minimal spanning tree a subgradient optimization procedure updates the lagrange multipliers we use fast sensitivity analysis techniques to increase the underlying graph sparsity and reduce the problem size the algorithm was tested on 416 problems with up to 500 cities and 10 salesmen we also present computational results on different data sets and parameters in order to identify the major factors that influence the performance of the developed code

mobility allowance shuttle transit mast services mip formulation and strengthening with logic constraints abstract we study a hybrid transportation system referred to as mobility allowance shuttle transit mast where vehicles may deviate from a fixed path consisting of a few mandatory checkpoints to serve demand distributed within a proper service area in this paper we propose a mixed integer programming mip formulation for the static scheduling problem of a mast type system since the problem is np hard we develop sets of logic cuts by using reasonable assumptions on passengers behavior the purpose of these constraints is to speed up the search for optimality by removing inefficient solutions from the original feasible region experiments show the effectiveness of the developed inequalities achieving a reduction up to 90 of the cpu solving time for some of the instances

minimum directed 1 subtree relaxation for score orienteering problem score orienteering is a variant of the orienteering game where competitors start at a specified control point visit as many control points as possible and thereby collect prizes and return to the starting point within a prescribed amount of time the competitor with the highest amount of prizes wins the game in this paper we propose the minimum directed 1 subtree problem as a new relaxation to this problem and develop two methods to improve its lower bound we describe a cut and dual simplex method and a lagrangian relaxation method and construct an algorithm that combines these two methods in an appropriate way computational experiments are carried out to analyse the behavior of the proposed relaxation with respect to the characteristics of the test problems especially for large scale instances we find that the proposed relaxation is superior to the ordinary assignment relaxation

a heuristic algorithm for the asymmetric capacitated vehicle routing problem abstract we consider the asymmetric capacitated vehicle routing problem acvrp a particular case of the standard asymmetric vehicle routing problem arising when only the vehicle capacity constraints are imposed acvrp is known to be np hard and finds practical applications e g in distribution and scheduling in this paper we describe the extension to acvrp of the two well known clarke wright and fisher jaikumar heuristic algorithms we also propose a new heuristic algorithm for acvrp that starting with an initial infeasible solution determines the final set of vehicle routes through an insertion procedure as well as intea route and inter route arc exchanges the initial infeasible solution is obtained by using the additive bounding procedures for acvrp described by fischetti toth and vigo in 1992 extensive computational results on several classes of randomly generated test problems involving up to 300 customers and on some real instances of distribution problems in urban areas are presented the results obtained show that the proposed approach favourably compares with previous algorithms from the literature

strong convergence theorems for finitely many nonexpansive mappings abstract under the assumption that e is a reflexive banach space whose norm is uniformly geteaux differentiable and which has a weakly continuous duality mapping j with gauge function ceng cubiotti yao strong convergence theorems for finitely many nonexpansive mappings and applications nonlinear analysis 67 2007 1464 1473 introduced a new iterative scheme for a finite commuting family of nonexpansive mappings and proved strong convergence theorems about this iteration in this paper only under the hypothesis that e is a reflexive banach space which has a weakly continuous duality mapping j with gauge function and several control conditions about the iterative coefficient are removed we present a short and simple proof of the above theorem

the impact of non isotropic scattering and directional antennas on mimo multicarrier mobile communication channels in outdoor environments waves propagate non isotropically because of non uniform distribution of scatterers in addition directional antennas which are efficient for communication applications have considerable impact on the response of the communication channel the impact of non isotropic propagation and directional antennas is more significant when the system employs multiple antennas in this paper we propose a space time frequency cross correlation function ccf for multiple input multiple output multicarrier channels in a two dimensional 2d random scattering medium the expression of the ccf turns out to be a multiplication of three ccfs two of these terms characterize the impact of mobile station and base station respectively and are linear bessel expansions where the coefficients are given by the linear convolution of the fourier series coefficients fsc s of the employed antenna patterns and the fscs of the probability density function describing 2d non isotropic environment the third expression characterizes the impact of the wireless channel in the stationary case we derive the expression of the fading channel power spectrum cps in terms of the non isotropic pdf and antenna patterns using the expression of the ccf we also calculate coherence bandwidth cb coherence time ct as a function of carrier frequency time separations our numerical results show a good fit to the available experimental results obtained for the cb ct of realistic outdoor channels

effective metastability of halpern iterates in cat 0 spaces abstract this paper provides an effective uniform rate of metastability in the sense of tao on the strong convergence of halpern iterations of nonexpansive mappings in cat 0 spaces the extraction of this rate from an ineffective proof due to saejung is an instance of the general proof mining program which uses tools from mathematical logic to uncover hidden computational content from proofs this methodology is applied here for the first time to a proof that uses banach limits and hence makes a substantial reference to the axiom of choice

halpern s iteration in banach spaces abstract we prove strong convergence theorems for a sequence which is generated by halpern s iteration we also apply our result for finding zeros of an accretive operator our result improves the recent result of aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in a banach space nonlinear anal 67 2007 2350 2360 by removing some assumptions on the parameters finally we discuss the new sufficient condition studied by song y song a new sufficient condition for the strong convergence of halpern type iterations appl math comput 198 2 2008 721 728 y song new strong convergence theorems for nonexpansive nonself mappings without boundary conditions comput math appl 56 6 2008 1473 1478 and correct the main result of song and chai y song x chai halpern iteration for firmly type nonexpansive mappings nonlinear anal 71 10 2009 4500 4506

cluster based branching for the asymmetric traveling salesman problem abstract this paper presents a new branching scheme for the asymmetric traveling salesman problem atsp based on clusters a cluster is defined as a node set with the characteristic that there exists an optimal solution in which the nodes in the node set are visited consecutively the paper considers identification of clusters implementation of a cluster based branching scheme and cluster based dominance tests the new approach is implemented in a branch and bound algorithm using a well known additive bounding procedure considerable savings in computing time are obtained compared to previously published assignment based branch and bound algorithms for the atsp

blind identification of simo systems and simultaneous estimation of multiple time delays from hos based inverse filter criteria higher order statistics based inverse filter criteria ifc have been effectively used for blind equalization of single input multiple output simo systems recently chi and chen reported a relationship between the unknown simo system and the optimum equalizer designed by the ifc for finite signal to noise ratio snr in this paper based on this relationship an iterative fast fourier transform fft based nonparametric blind system identification bsi algorithm and an fft based multiple time delay estimation mtde algorithm are proposed with a given set of non gaussian measurements the proposed bsi algorithm allows the unknown simo system to have common subchannel zeros and its performance estimation accuracy is superior to that of the conventional ifc based methods the proposed mtde algorithm can simultaneously estimate all the p 1 time delays with respect to a reference sensor with space diversity of sensors exploited therefore its performance estimation accuracy is robust to the nonuniform distribution of snrs of p spl ges 2 sensors due to channel fading some simulation results are presented to support the efficacy of the proposed bsi algorithm and mtde algorithm

on convergence criteria of generalized proximal point algorithms we analyze some generalized proximal point algorithms which include the previously known proximal point algorithms as special cases weak and strong convergence of the proposed proximal point algorithms are proved under some mild conditions

the cross bicepstrum definition properties and application for simultaneous reconstruction of three nonminimum phase signals the recovery of three signals from their cross bispectrum or the identification of the impulse responses of three parallel linear time invariant lti systems from the cross bispectrum of their system outputs by computing the complex cepstrum of the cross bispectrum as long as the signals or impulse responses have no zeros on the unit circle is discussed it is shown that the three signals can be separated completely and approximately recovered in the cross bicepstrum domain except for their magnitude and linear phase factors the computation of the cross bicepstrum can be seen as a method for the simultaneous computation of the ordinary complex cepstra of three nonminimum phase signals without the need for phase unwrapping both least squares and fast fourier transform fft based methods for computing the bicepstral coefficients are presented simulation examples of signal reconstruction in gaussian white and nongaussian colored noise and of system identification are included the results are extended to nth order cross spectra and the factorization problem for these spectra is discussed

iterative construction for common fixed points of finitely many nonexpansive mappings abstract many problems encountered in applied mathematics can be recast as the problem of selecting a particular common fixed point of a family of nonexpansive mappings in a banach space in this paper under the hypotheses that e is a reflexive and strictly convex banach spaces with a uniformly g eaux differentiable norm the strong convergence of a iteration algorithm is proved for finding a common fixed point of a finite family of nonexpansive self mappings defined on a closed convex subset k of e

the tree representation for the pickup and delivery traveling salesman problem with lifo loading the feasible solutions of the traveling salesman problem with pickup and delivery tsppd are commonly represented by vertex lists however when the tsppd is required to follow a policy that loading and unloading operations must be performed in a last in first out lifo manner we show that its feasible solutions can be represented by trees consequently we develop a novel variable neighborhood search vns heuristic for the tsppd with last in first out loading tsppdl involving several search operators based on the tree data structure extensive experiments suggest that our vns heuristic is superior to the current best heuristics for the tsppdl in terms of solution quality while requiring no more computing time as the size of the problem increases

an empirical study of a new metaheuristic for the traveling salesman problem abstract we present a deceptively simple yet empirically powerful metaheuristic called jump search for solving traveling salesman problems that has been found to be more effective than tabu search on both random and benchmark test problems from the literature while the underlying philosophy of jump search applying local search from different starting points has been discussed in the literature previously using random starting points the use of construction based heuristic solutions has heretofore not been considered extensive empirical analysis shows the method to be surprisingly effective vis a vis a randomized strategy and in comparison with tabu search the approach is quite robust and suggests that a systematic search among neighborhoods of good not random solutions provides distinct advantages this suggests that further research be focused on better construction heuristics and hybrid schemes that incorporate jump search in for example tabu search

an improved transformation of the symmetric multiple traveling salesman problem we improve the standard transformation of the symmetric single depot multiple traveling salesman problem mtsp to one on a sparser edge configuration the improvement tends to suppress to a large extent the degeneracy of the resulting symmetric traveling salesman problem tsp as a result a 1 tree based tsp algorithm solves large mtsps of the type we consider as easily as it solves standard tsps we demonstrate the improvement by presenting computational results that are currently the best available

strong convergence for a countable family of strict pseudocontractions in q uniformly smooth banach spaces we introduce a new iterative algorithm for finding a common fixed point of a countable family of strict pseudocontractions in q uniformly smooth and uniformly convex banach spaces we then prove that the sequence generated by the proposed algorithm converges strongly to a common fixed point of an infinite family of strict pseudocontractions our results mainly improve and extend the results announced by yao et al y yao y c liou g marino strong convergence of two iterative algorithms for nonexpansive mappings in hilbert spaces fixed point theory appl 2009 2009 7 pages doi 10 1155 2009 279058 art id 279058

the symmetric traveling salesman problem and edge exchanges in minimal 1 trees abstract in this article the effect of exchanging edges inside a minimal 1 tree with edges outside is analysed in combination with an upper bound this analysis enables the elimination of variables in the symmetric traveling salesman problem after discussion on a number of improvements for this analysis the implementation is described in a traveling salesman algorithm based on the 1 tree relaxation computational results show the advantages of the edges exchanges for euclidean problems up to 120 cities as well as for random table problems up to 200 cities

multichannel adaptive blind deconvolution using the complex cepstrum of higher order cross spectra an adaptive cross spectral blind deconvolution method cross tea for the case in which data are available from several sensors is described unlike ordinary cross spectra higher order cross spectra are separable and this fact is used to identify and deconvolve each system cross tea was tested on four channel qam quadrature amplitude modulation signals and the results are compared to those for tea an autospectral method

an effective implementation of the lin kernighan traveling salesman heuristic abstract this paper describes an implementation of the lin kernighan heuristic one of the most successful methods for generating optimal or near optimal solutions for the symmetric traveling salesman problem tsp computational tests show that the implementation is highly effective it has found optimal solutions for all solved problem instances we have been able to obtain including a 13 509 city problem the largest non trivial problem instance solved to optimality today

four parameter proximal point algorithms several strong convergence results involving two distinct four parameter proximal point algorithms are proved under different sets of assumptions on these parameters and the general condition that the error sequence converges to zero in norm thus our results address the two important problems related to the proximal point algorithm one being that of strong convergence instead of weak convergence and the other one being that of acceptable errors one of the algorithms discussed was introduced by yao and noor 2008 7 while the other one is new and it is a generalization of the regularization method initiated by lehdili and moudafi 1996 9 and later developed by xu 2006 8 the new algorithm is also ideal for estimating the convergence rate of a sequence that approximates minimum values of certain functionals although these algorithms are distinct it turns out that for a particular case they are equivalent the results of this paper extend and generalize several existing ones in the literature

a branch first cut second approach for locomotive assignment the problem of assigning locomotives to trains consists of selecting the types and number of engines that minimize the fixed and operational locomotive costs resulting from providing sufficient power to pull trains on fixed schedules the force required to pull a train is often expressed in terms of horsepower and tonnage requirements rather than in terms of number of engines this complicates the solution process of the integer programming formulation and usually creates a large integrality gap furthermore the solution of the linearly relaxed problem is strongly fractional to obtain integer solutions we propose a novel branch and cut approach the core of the method consists of branching decisions that define on one branch the projection of the problem on a low dimensional subspace there the facets of the polyhedron describing a restricted constraint set can be easily derived we call this approach branch first cut second we first derive facets when at most two types of engines are used we then extend the branching rule to cases involving additional locomotive types we have conducted computational experiments using actual data from the canadian national railway company simulated test problems involving two or more locomotive types were solved over 1 2 and 3 day rolling horizons the cuts were successful in reducing the average integrality gap by 52 for the two type case and by 34 when more than 25 types were used furthermore the branch first cut second approach was instrumental in improving the best known solution for an almost 2 000 leg weekly problem involving 26 locomotive types it reduced the number of locomotives by 11 or 1 1 at an equivalent savings of 3 000 000 per unit additional tests on different weekly data produced almost identical results

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

new lower bounds for the symmetric travelling salesman problem in this paper new lower bounds for the symmetric travelling salesman problem are proposed and combined in additive bounding procedures efficient implementations of the algorithms are given in particular fast procedures for computing the linear programming reduced costs of the shortest spanning tree sst problem and for finding all ther sst of a given graph are presented computational results on randomly generated test problems are reported

an additive bounding procedure for the asymmetric travelling salesman problem in this paper new lower bounds for the asymmetric travelling salesman problem are presented based on spanning arborescences the new bounds are combined in an additive procedure whose theoretical performance is compared with that of the balas and christofides procedure 1981 both procedures have been imbedded in a simple branch and bound algorithm and experimentally evaluated on hard test problems

a branch and cut algorithm for the symmetric generalized traveling salesman problem we consider a variant of the classical symmetric traveling salesman problem in which the nodes are partitioned into clusters and the salesman has to visit at least one node for each cluster this np hard problem is known in the literature as the symmetric generalized traveling salesman problem gtsp and finds practical applications in routing scheduling and location routing in a companion paper fischetti et al fischetti m j j salazar p toth 1995 the symmetric generalized traveling salesman polytope networks 26 113 123 we modeled gtsp as an integer linear program and studied the facial structure of two polytopes associated with the problem here we propose exact and heuristic separation procedures for some classes of facet defining inequalities which are used within a branch and cut algorithm for the exact solution of gtsp heuristic procedures are also described extensive computational results for instances taken from the literature and involving up to 442 nodes are reported

a multiplier adjustment method for the generalized assignment problem we describe a branch and bound algorithm for the generalized assignment problem in which bounds are obtained from a lagrangian relaxation with the multipliers set by a heuristic adjustment method the algorithm was tested on a large sample of small random problems and a number of large problems derived from a vehicle routing application computation times were reasonable in all cases and the branch and bound trees generated had nearly two orders of magnitude fewer nodes than for competing algorithms although comparison of running times on different machines is difficult the multiplier adjustment method appears to be about one order of magnitude faster than the best previously existing algorithms for this problem

a dual ascent approach for steiner tree problems on a directed graph the steiner tree problem on a directed graph stdg is to find a directed subtree that connects a root node to every node in a designated node setv we give a dual ascent procedure for obtaining lower bounds to the optimal solution value the ascent information is also used in a heuristic procedure for obtaining feasible solutions to the stdg computational results indicate that the two procedures are very effective in solving a class of stdg s containing up to 60 nodes and 240 directed 120 undirected arcs