design of two dimensional digital filters using singular value decomposition and balanced approximation method it is shown that the singular value decomposition svd of the sampled amplitude response of a two dimensional 2 d digital filter possesses a special structure every singular vector is either mirror image symmetric or antisymmetric with respect to its midpoint consequently the svd can be applied along with 1 d finite impulse response fir techniques for the design of linear phase 2 d filters with arbitrary prescribed amplitude responses which are symmetrical with respect to the origin of the omega psi omega sub 2 plane the balanced approximation method is applied to linear phase 2 d fir filters of the type that may be obtained by using the svd method the method leads to economical and computationally efficient filters usually infinite impulse response filters which have prescribed amplitude responses and whose phase responses are approximately linear

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 unified theory for formulation of hybrid stress membrane elements a theory is proposed in this paper to explain in a unified manner the three rational approaches using the incompatible displacements u in the hybrid element formulation limited to the plane stress case the theory suggests that the introduction of u is to constrain the total value of the invariant i2 x y of the assumed stresses over the element to zero in the plane stress case this is the well known condition for the stress distributions to be independent of the elastic constants of the material the theory proposed is also used to explain the closeness of the performances of the four 4 node hybrid stress membrane elements 5 i 5 ii 5 a and 5 c that have been developed previously the differences among them are shown to be of the second degree in the distortion measures of the element shape when they are compared on the basis of the non vanishing total value of i2 of their respectively adopted assumed stress field several numerical examples are used to verify and to illustrate the proposed theory

efficient design of digital filters for 2 d and 3 d depth migration two and three dimensional 2 d and 3 d depth migration can be performed using 1 d and 2 d extrapolation digital filters respectively the depth extrapolation is done one frequency at a time by convolving the seismic wavefield with a complex valued frequency and velocity dependent digital filter this process requires the design of a complete set of extrapolation filters one filter for each possible frequency velocity pair instead of independently designing the frequency and velocity dependent filters an efficient procedure is introduced for designing a complete set of 1 d and 2 d extrapolation filters using transformations the problem of designing a desired set of migration filters is thus reduced to the design of a single 1 d filter which is then mapped to produce all the desired 1 d or 2 d migration filters the new design procedure has the additional advantage that both the 1 d and 2 d migration filters can be realized efficiently and need not have their coefficients precomputed or tabulated

algorithms for a multi level network optimization problem in this paper we work on a multi level network optimization problem that integrates into the same model important aspects of i discrete facility location ii topological network design and iii network dimensioning potential applications for the model are discussed stressing its growing importance the multi level network optimization problem treated is defined and a mathematical programming formulation is presented we make use of a branch and bound algorithm based on lagrangean relaxation lower bounds to introduce some new powerful auxiliary algorithms to exactly solve the problem we conduct a set of computational experiments that indicate the quality of the proposed approach

stable explicit depth extrapolation of seismic wavefields stable explicit filters for depth extrapolation of seismic wavefields may be derived through a modification of the conventional taylor series method the modified taylor series method described here yields extrapolators with maximally flat amplitude spectra in their passband while ensuring that no spectral components in the wavefield are amplified by any factor greater than one the price for stability is increased phase error for low normalized frequencies implicit extrapolators are more accurate than the 39 coefficient stable explicit extrapolator described here however the small spatial sampling intervals required to obtain high phase accuracy in implicit extrapolation imply that this accuracy is rarely achieved in practice over the wide range of normalized frequencies likely to be encountered in practice stable explicit extrapolators outperform implicit ones the method presented here for deriving stable explicit extrapolators is in no formal sense optimal it is only guaranteed to yield stable extrapolators in my limited experience with alternative methods for designing stable extrapolators the method presented here produced the least phase error while ensuring stability nevertheless a simple method for designing optimal in some sense stable explicit extrapolators would be preferred over the method presented here 7 refs 15 figs

generating alternative mixed integer programming models using variable redefinition dropping the complicating constraints in a mixed integer linear program often yields a special structure subproblem that can be reformulated using a different set of decision variables once the new variables have been identified the entire problem can be reformulated in terms of the new variables we develop a theory of variable redefinition based on relating the two sets of decision variables by a linear transformation and describe methods for reformulating the special structure problem the reformulated models have a more accurate linear relaxation than the problems from which they were derived an important property within the context of linear programming based branch and bound modeling approaches

new stress assumption for hybrid stress elements and refined four node plane and eight node brick elements a new stress assumption for hybrid stress elements is presented generalized incompatible modes are proposed and incorporated into the constraint equations for assumed stresses the physical meaning of the resulting constraint equations is discussed the present stress assumption which can consider the mesh distortion more rigorously is based on the physical interpretation of the role of the generalized incompatible modes and substantiated with simple mesh distortion measures defined in this paper the stress assumption is adapted to the previous four node hybrid stress element 5 i and the eight node hybrid stress brick element 18 which results in a new four node plane element m5 and an new eight node brick element m18 numerical results show that the refined elements are noticeable in low sensitivity to mesh distortion and in high accuracy of stresses 1997 john wiley sons ltd

a constrained nonlinear 0 1 program for data allocation abstract this paper analyzes the problem of allocating copies of relations from a global database to the sites of a geographically distributed communication network the objective of the allocation is to minimize the total cost due to transmissions generated by queries from the various sites including queries that access multiple relations this allocation problem is modeled as a constrained nonlinear 0 1 subproblems generated during subgradient optimization are solved as optimization some of the unconstrained quadratic 0 1 subproblems generated during subgradient optimization are solved as maximum flow problems while the others require implicit enumeration depending on the nature of the objective function coefficients of the subproblems our solution approach is tested extensively on data allocation problems with as many as 100 sites and 20 relations on a set of randomly generated test problems our approach was close to two orders of magnitude faster than the general purpose integer programming code osl

a lagrangean relaxation approach for very large scale capacitated lot sizing in this paper we develop a lagrangean relaxation based heuristic procedure to generate near optimal solutions to very large scale capacitated lot sizing problems clsp with setup times and limited overtime our computational results show that large problems involving several thousand products and several thousand 0 1 integer variables can be solved in a reasonable amount of computer time to within one percent of their optimal solution the proposed procedure is general enough to be applied directly or with slight modification to real life production problems

capacitated multi item lot sizing problems with time windows this research concerns a new family of capacitated multi item lot sizing problems namely lot sizing problems with time windows two classes of the problem are analyzed and solved using different lagrangian heuristics capacity constraints and a subset of time window constraints are relaxed resulting in particular single item time window problems that are solved in polynomial time other relaxations leading to the classical wagner whitin problem are also tested several smoothing heuristics are implemented and tested and their results are compared the gaps between lower and upper bounds for most problems are very small less than 1 moreover the proposed algorithms are robust and do not seem to be too affected when different parameters of the problem are varied

three different criteria for the design of two dimensional zero phase fir digital filters an error criterion for the design of fir filters is proposed filters with relatively many free filter coefficients are designed using the chebyshev the weighted least squares wls and a new partitioned minimax error criterion and the performance of the filters is compared a general and fast technique for the wls design is also presented

heuristics for multilevel lot sizing with a bottleneck in this paper we present a heuristic method based on lagrangian relaxation for multilevel lot sizing when there is a single bottleneck facility a series of lagrangian relaxations one for each item in the product structure is imbedded in a branch and bound procedure the objective is to find a production schedule that fits within available capacity at minimum cost the method has two solution phases dual and primal in the dual phase of the procedure implied costs of setups and production are determined based on a tentative schedule the primal phase is repeated with these new prices and we iterate to reach a good solution the solution procedure is first tested on two special cases uncapacitated multilevel lot sizing and the capacitated single level multi item lot sizing problem the results show that the solution procedure can provide better solutions than some heuristics designed especially for those problems test results on the bottleneck problem indicate that good feasible solutions are found for problems too difficult to solve with exact methods

a computational method for the lu decomposition of rectangular matrices and its implications to the realization of 2 d digital filters the realization of 2 d digital filters based on the lower upper triangular decomposition of the coefficient matrix is investigated a numerical method based on the qa decomposition which has some important characteristics is proposed for reaching the lu structure the coefficients in the final lu structure have values favorable to fixed point arithmetic implementation furthermore the qr structure can be used for the realization and possesses good numerical characteristics in terms of the approximate decomposition scheme the symmetry in the impulse response coefficient matrix of an octagonally symmetric 2 d fir filter is utilized to reduce the computational effort spent in the decomposition and the total number of multipliers in the final realization structure

simultaneous lotsizing and scheduling by combining local search with dual reoptimization abstract the contribution of this paper is twofold on the one hand the particular problem of integrating lotsizing and scheduling of several products on a single capacitated production line is modelled and solved taking into account sequence dependent setup times thereby continuous lotsizes meeting deterministic dynamic demands are to be determined and scheduled with the objective of minimizing inventory holding costs and sequence dependent setup costs on the other hand a new general algorithmic approach is presented a dual reoptimization algorithm is combined with a local search heuristic for solving a mixed integer programming problem this idea is applied to the above lotsizing and scheduling problem by embedding a dual network flow algorithm into threshold accepting and simulated annealing respectively computational tests show the effectiveness of the new solution method

the geometry of weighted low rank approximations the low rank approximation problem is to approximate optimally with respect to some norm a matrix by one of the same dimension but smaller rank it is known that under the frobenius norm the best low rank approximation can be found by using the singular value decomposition svd although this is no longer true under weighted norms in general it is demonstrated here that the weighted low rank approximation problem can be solved by finding the subspace that minimizes a particular cost function a number of advantages of this parameterization over the traditional parameterization are elucidated finding the minimizing subspace is equivalent to minimizing a cost function on the grassmann manifold a general framework for constructing optimization algorithms on manifolds is presented and it is shown that existing algorithms in the literature are special cases of this framework within this framework two novel algorithms a steepest descent algorithm and a newton like algorithm are derived for solving the weighted low rank approximation problem they are compared with other algorithms for low rank approximation as well as with other algorithms for minimizing a cost function on a grassmann manifold

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

efficient realizations of two dimensional quadratic digital filters realization structures of two dimensional finite support quadratic digital filters which are based on matrix decomposition are introduced the resulting structures consist generally of a number of parallel branches which operate simultaneously and independently on a common input array by proper decomposition of the coefficient matrix each parallel branch can be realized by a two dimensional finite impulse response digital filter in cascade with a squaring operator the lower upper triangular decomposition and the singular value lower upper decomposition is used in order to arrive at efficient structures with computational and hardware advantages

exact and approximation algorithms for the operational fixed interval scheduling problem the operational fixed interval scheduling problem ofisp is characterized as the problem of scheduling a number of jobs each with a fixed starting time a fixed finishing time a priority index and a job class the objective is to find an assignment of jobs to machines with maximal total priority the problem is complicated by the restrictions that i each machine can handle only one job at a time ii each machine can handle only jobs from a prespecified subset of all possible job classes and iii preemption is not allowed it follows from the above that ofisp has both the character of a job scheduling problem and the character of an assignment problem in this paper we discuss the occurrence of the problem in practice and we present newly developed exact and approximation algorithms for solving ofisp finally some computational results are shown

a decomposition theorem and its implications to the design and realization of two dimensional filters it is shown that an arbitrary rational 2 d transfer function can be expanded in first order terms each one of which is a function of only one of the two variables this method leads naturally to reconfigurable filters with great modularity and parallelism which can realize any rational transfer function up to a given order

optimal design of iir digital filters with robust stability using conic quadratic programming updates in this paper minimax design of infinite impulse response iir filters with prescribed stability margin is formulated as a conic quadratic programming cqp problem cqp is known as a class of well structured convex programming problems for which efficient interior point solvers are available by considering factorized denominators the proposed formulation incorporates a set of linear constraints that are sufficient and near necessary for the iir filter to have a prescribed stability margin a second order cone condition on the magnitude of each update that ensures the validity of a key linear approximation used in the design is also included in the formulation and eliminates a line search step collectively these features lead to improved designs relative to several established methods the paper then moves on to extend the proposed design methodology to quadrantally symmetric two dimensional 2 d digital filters simulation results for both one dimensional 1 d and 2 d cases are presented to illustrate the new design algorithms and demonstrate their performance in comparison with several existing methods

designing stable extrapolators for explicit depth extrapolation of 2d and 3d wavefields using projections onto convex sets we have developed a robust algorithm for designing explicit depth extrapolation operators using the projections onto convex sets pocs method the operators are optimal in the sense that they satisfy all required extrapolation design characteristics in addition we propose a simple modification of the pocs algorithm modified pocs or mpocs that further enhances the stability of extrapolated wavefields and reduces the number of iterations required to design such operators to approximately 2 of that required for the basic pocs design algorithm various synthetic tests show that 25 coefficient 1d extrapolation operators which have 13 unique coefficients can accommodate dip angles up to 70 we migrated the seg eage salt model data with the operators and compare our results with images obtained via extrapolators based on modified taylor series and with wavefield extrapolation techniques such as phase shift plus interpolation pspi and split step fourier the mpocs algorithm provides practically stable

efficient implementations of quadratic digital filters efficient implementation structures of quadratic filters are introduced in this paper using systolic arrays distributed arithmetic and linear convolutions with multipliers the implementations are based on matrix decompositions and consist of a set of parallel 1 d fir filters in cascade with a set of sequential square in add out type of operations the structures are compared using various realistic figures of merit such as data throughput delay cost that is proportional to chip area and variance of roundoff errors in the filter output assuming fixed point arithmetic for comparison purposes the direct and biglieri quadratic structures are included in this study evaluating the comparative results the conclusion drawn is that the matrix decomposition realization of a quadratic filter implemented with systolic arrays seems to be offering the best compromise among the various conflicting figures of merit

studying the effects of production loss due to setup in dynamic production scheduling abstract we study the effects of production loss during setup in dynamic production scheduling for process industries producing several products on non identical flexible processors the production scheduling problem is formulated as a mixed integer programming model and solved using primal and dual lagrangean based procedures real data from a tile company and randomly generated data were used to test the model our computational results show the solution procedure to be fast robust and stable even for cases with large setup costs and production losses and for cases with demands of up to 52 periods

alternative ways for formulation of hybrid stress elements an element stiffness matrix can be derived by the conventional potential energy principle and indirectly also by generalized variational principles such as the hu washizu principle and the hellinger reissner principle the present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the hellinger reissner principle it is found that the resulting scheme is equivalent to that considered by tong 1982 for the construction of hybrid stress elements in tong s scheme the inversion of a large flexibility matrix can be avoided it is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the hellinger reissner principle and the hu washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method

an efficient algorithm for the lagrangean dual of nonlinear knapsack problems with additional nested constraints abstract this paper presents an efficient algorithm for solving the lagrangean dual of nonlinear knapsack problems with additional nested constraints the dual solution provides a feasible primal solution if it exists and associated lower and upper bounds on the optimal objective function value of the primal problem computational experience is cited indicating computation time number of dual iterations and tightness of the bounds

a method for the cutting stock problem with different qualities abstract an operations research project at a swedish company is reported the project deals with the problem of allocating wood products with different quality requirements to be cut from wooden boards which in turn consists of a number of quality zones a major difficulty is the existence of distinct time limits since the cross cutting of the boards is done in a real time process in this paper we derive a mathematical model which includes a set packing problem that accurately describes the real world problem this problem is then solved using a combination of lagrangean relaxation and subgradient optimization numerical results for practical problems are reported the results indicate a valid model and satisfactory efficiency of the proposed solution procedure

facilities location in a competitive environment a promethee based multiple criteria analysis abstract in this paper a methodology for locating facilities in a competitive environment is introduced in this methodology the multi criteria approach and the notion of efficiency are appropriately integrated the classic distance criterion is combined with a second one a quality criterion to produce a more realistic representation of a customer s decision process

a rational approach for choosing stress terms for hybrid finite element formulations a new approach for choosing the stress terms for hybrid stress elements is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacements examples using 4 node plane stress elements have shown that when the incompatible displacements also satisfy the constant strain patch test the resulting element will provide the most accurate solutions

on the incompressible constraint of the 4 node quadrilateral element the standard plane 4 node element is written as the summation of a constant gradient matrix usually obtained from underintegration and a stabilization matrix the split is based on a taylor series expansion of element basis functions in the incompressible limit the locking effect of the quadrilateral is traced back to the stabilization matrix which reflects the incomplete higher order term in the taylor series the incompressibility condition is formulated in a weak sense so that the element displacement field is divergence free when integrated over the element volume the resulting algebraic constraint is shown to coincide with a particular eigenvector of the constant gradient matrix which is obtained from the first order terms of the taylor series the corresponding eigenvalue enforces incompressibility implicitly by means of a penalty constraint analytical expressions for that constant dilatation eigenpair are derived for arbitrary element geometries it is shown how the incompressible constraint carries over to the element stiffness matrix if the element stabilization is performed in a particular manner for several classical and recent elements the eigensystems are analysed numerically it is shown that most of the formulations reflect the incompressible constraint identically in the incompressible limit the numerical accuracies of the elements are compared

separable denominator state space realization of two dimensional filters using a canonic form in this paper a procedure is developed for the computation of a state space realization of a two dimensional filter the transfer function of this realization has a separable denominator the procedure relies on a canonic form for the state space realization and utilizes a finite sequence of two dimensional pulse response coefficients markov parameters

development and testing of stable invariant isoparametric curvilinear 2 and 3 d hybrid stress elements abstract linear and quadratic serendipity hybrid stress elements are examined in respect of stability coordinate invariance and optimality a formulation based upon symmetry group theory successfully addresses these issues in undistorted geometries and is fully detailed for plane elements the resulting least order stable invariant stress polynomials can be applied as astute approximations in distorted cases through a variety of tensor components and variational principles a distortion sensitivity study for two and three dimensional elements provides favourable numerical comparisons with the assumed displacement method

realization of 2 d linear phase fir filters by using the singular value decomposition the singular value decomposition svd technique is investigated for the realization of a general two dimensional 2 d linear phase fir filter with an arbitrary magnitude response a parallel realization structure consisting of a number of one dimensional 1 d fir subfilters is obtained by applying the svd to the impulse response of a 2 d filter it is shown that by using the symmetry property of the 2 d impulse response and by developing an appropriate unitary transformation an svd yielding linear phase constituent 1 d filters can always be obtained so that the efficient structures of the 1 d linear phase filters can be exploited for 2 d realization it is shown that when the 2 d filter to be realized has some specified symmetry in its magnitude response the proposed svd realization would yield a magnitude characteristic with the same symmetry an analysis is carried out to obtain tight upper bounds for the errors in the impulse response as well as in the frequency response of the realized filter it is shown that the number of parallel sections can be reduced significantly without introducing large errors even in the case of 2 d filters with nonsymmetric magnitude response

using confidence limits for the global optimum in combinatorial optimization let z be the unknown optimal value of a combinatorial optimization problem in minimization form and let z be a constant satisfying probz z 1 for a fixed 0 1 then z is called a statistical or probabilistic lower bound at significance level 1 we discuss how statistical lower bounds can be used to measure the effectiveness of an approximate solution and to fathom subproblems in a branch and bound approach after reviewing some methods for obtaining statistical lower bounds we report on extensive computational experience for two notoriously difficult combinatorial optimization problems the traveling salesman problem and the quadratic assignment problem from our experience we conclude that statistical bounds are highly useful for quadratic assignment problems in this problem context the quality of simple analytic formulas is comparable to the quality of the maximum likelihood formula in general using statistics to aid in the solution of combinatorial optimization problems should be most useful when such problems are large

a decomposition approach for the general lotsizing and scheduling problem for parallel production lines abstract this paper presents a novel solution heuristic to the general lotsizing and scheduling problem for parallel production lines glsppl the glsppl addresses the problem of simultaneously deciding about the sizes and schedules of production lots on parallel heterogeneous production lines with respect to scarce capacity sequence dependent setup times and deterministic dynamic demand of multiple products its objective is to minimize inventory holding sequence dependent setup and production costs the new heuristic iteratively decomposes the multi line problem into a series of single line problems which are easier to solve different approaches for decomposition and for the iteration between a modified multi line master problem and the single line subproblems are proposed they are compared with an existing solution method for the glsppl by means of medium sized and large practical problem instances from different types of industries the new methods prove to be superior with respect to both solution quality and computation time

realisation and approximation of linear infinite dimensional systems with error bounds the class of linear infinite dimensional systems with finite dimensional inputs and outputs whose impulse response h satisfies h in l 1 cap l 2 0 infty mathbb c p times m and induces a nuclear hankel operator is said to be of nuclear type for this class of systems it is shown that balanced or output normal realisations always exist and their truncations converge to the original system in various topologies furthermore explicit l infty bounds on the transfer function errors l 1 and l 2 bounds on the impulse response errors and hilbert schmidt and nuclear bounds on the hankel operator errors are obtained these truncations also generate an approximating sequence to the optimal hankel norm approximations to the original system and various error bounds of these approximants are deduced

implementation of 2d explicit depth extrapolation fir digital filters for 3d seismic volumes using singular value decomposition we propose a new scheme for implementing predesigned 2d complex valued wavefield extrapolation finite impulse response fir digital filters which are used for extrapolating 3d seismic wavefields the implementation is based on singular value decomposition svd of quadrantally symmetric 2d fir filters extrapolators to simplify the svd computations for such afilter impulse response structure we apply a special matrix transformation on the extrapolation fir filter impulse responses where we guarantee the retentionoftheirwavenumberphaseresponse unliketheexisting 2d fir filter implementation methods that are used for this geophysical application such as the mcclellan transformationoritsimprovedversion thisimplementationviasvdresults in perfect circularly symmetrical magnitude and phase wavenumber responses in this paper we also demonstrate that the svd method can save depending on the filter size more than 23 of the number of multiplications per output sample and approximately 62 of the number of additions per output sample when compared to direct implementation with quadrantal symmetry via true 2d convolution finally anapplicationtoextrapolationofaseismicimpulseisshown toproveourtheoreticalconclusions

explicit 3 d migration using equiripple polynomial expansion and laplacian synthesis in f x explicit finite difference depth migration schemes wavefield downward extrapolation is carried out through spatial convolution using finite length filters existing methods for computing these filters are based on nonlinear least squares with a high computational cost or on taylor series expansion which is suboptimal in the 3 d case the physics of wavefield extrapolation requires 2 d extrapolation filters with circular symmetry recently mcclellan transformation has been used to design circularly symmetric extrapolation operators but this approach exhibits artifacts when the data are not spatially oversampled we describe an alternative method to take advantage of the circular symmetry the radial response of the filter is expanded as a polynomial in the laplacian which is synthesized as the sum of two 1 d second derivative filters using the laplacian rather than the mcclellan transform yields an artifact free impulse response for wavenumbers much closer to the nyquist wavenumber at the s

extension of field consistence approach into developing plane stress elements in this research paper the possibilities for extending the field consistence approach l yunhua on shear locking in finite elements licentiate thesis stockholm 1997 l yunhua explanation and elimination of shear locking and membrane locking with field consistence approach comput methods appl mech engrg in press starting from different variational principles to plane stress elements are investigated in the extension two main difficulties are explicitly solving a set of coupled partial differential equations and satisfying inter element compatibility the first one is alleviated by constructing element interpolations from a set of quasi general solutions rather than the real general solutions to the euler lagrangian equations the second one is solved by combining the field consistence approach with the iso parametric interpolation technique the traditional assumed stress method is improved and an efficient plane stress element is obtained it seems that the relations between the three commonly used variational principles can be more reasonably established in the framework of the field consistence approach

l sub 2 sensitivity analysis and minimization of 2 d separable denominator state space digital filters for two dimensional 2 d state space digital filters that are separable in the denominator the coefficient sensitivity is analyzed by using a pure l sub 2 norm and then the problem of minimizing the l sub 2 sensitivity is considered first a novel expression is developed in closed form for the evaluation of the l sub 2 sensitivity next an iterative procedure is presented for synthesizing the optimal filter structures that minimize the l sub 2 sensitivity finally a numerical example is given to illustrate the utility of the proposed technique

the lu decomposition theorem and its implications to the realization of two dimensional digital filters a new approach to the realization of two dimensional 2 d fir and iir digital filters is introduced based on the so called lower upper triangular lu decomposition of matrix coefficients of their two dimensional polynomials it is demonstrated that the lu realization scheme enjoys a number of attributes for vlsi implementation including high parallelism modularity and regularity this paper also shows that the computational requirements of the lu realization structure are much smaller than those of the jordan jd singular value sv and canonical direct realizations furthermore it is shown that if a canonical 2 d iir filter is realizable then a realizable lu decomposition form can be always obtained a property that is not shared by the jd and sv decomposition forms finally the extension of the lu decomposition approach to the realization of m d digital filters is discussed

capacitated lot sizing and scheduling by lagrangean relaxation abstract development of new models and solution procedures for production planning has been of research interest for several decades implementation of these models has resulted in lower production costs by reducing inventories number of setups and labor costs in this paper we develop several optimal near optimal procedures for the capacitated lot sizing and scheduling problem clsp with setup times limited regular time and limited overtime we formulate a mixed integer linear programming model of the problem and solve it by lagrangean relaxation we experiment with alternative lagrangean relaxations and develop new procedures to solve these relaxations overall the capacity constraints relaxation seems to be superior to the demand constraints relaxation our results show that large problems can be solved in reasonable computer times and within one percent accuracy of the optimal solutions we solved 99 8 i e 99 items and 8 periods 50 12 and 50 8 problems in 30 61 36 25 and 12 65 seconds of cdc cyber 730 computer time respectively our procedures are general enough to be applied directly or with slight modifications in real life production settings

block 2 d interpolation efficient matrix factorization and application to signal processing a block 2 d decomposition and a new block lu matrix factorization based on a newton approach are presented for solving quickly and efficiently polynomial or exponential 2 d interpolation problems the sample grids under consideration are described by the product representation x sub 0 x sub 1 x sub n x y sub 0 y sub 1 y sub m where the x grid and the y grid are not necessarily uniformly spaced the attractive features of the method are the inherent efficient parallelism the reduced computational requirements needed for the lu decomposition and the capability of implementation of 1 d fast and accurate algorithms the proposed method can be used for modeling 2 d discrete signals designing 2 d fir filters 2 d fourier matrix factorization 2 d dft etc

dynamic aggregation of set partitioning constraints in column generation column generation is often used to solve problems involving set partitioning constraints such as vehicle routing and crew scheduling problems when these constraints are in large numbers and the columns have on average more than 8 12 nonzero elements column generation often becomes inefficient because solving the master problem requires very long solution times at each iteration due to high degeneracy to overcome this difficulty we introduce a dynamic constraint aggregation method that reduces the number of set partitioning constraints in the master problem by aggregating some of them according to an equivalence relation to guarantee optimality this equivalence relation is updated dynamically throughout the solution process tests on the linear relaxation of the simultaneous vehicle and crew scheduling problem in urban mass transit show that this method significantly reduces the size of the master problem degeneracy and solution times especially for larger problems in fact for an instance involving 1 600 set partitioning constraints the master problem solution time is reduced by a factor of 8

highly molecular systolic structures for denominator separable 2 d recursive filters two systolic realization structures for the implementation of 2 d denominator separable recursive filters are presented these structures possess a high degree of modularity and parallelism with low roundoff noise the number of delays and multipliers is fewer than for similar realizations in the literature the proposed structures are more suitable for special purpose hardware and amenable to vlsi design

a multiperiod two echelon multicommodity capacitated plant location problem abstract in this paper we deal with a facility location problem where one desires to establish facilities at two different distribution levels by selecting the time periods our model intends to minimize the total cost for meeting demands for all the products specified over the planning horizon at various customer locations while satisfying the capacity requirements of the production plants and intermediate warehouses we address this problem by means of a formulation as a mixed integer programming problem a lagrangean relaxation is proposed to solve the problem together with a heuristic procedure that constructs feasible solutions of the original problem from the solutions at the lower bounds obtained by the relaxed problems computational tests are provided showing the good performance of this approach for a wide range of problems

meta heuristics for dynamic lot sizing a review and comparison of solution approaches proofs from complexity theory as well as computational experiments indicate that most lot sizing problems are hard to solve because these problems are so difficult various solution techniques have been proposed to solve them in the past decade meta heuristics such as tabu search genetic algorithms and simulated annealing have become popular and efficient tools for solving hard combinatorial optimization problems we review the various meta heuristics that have been specifically developed to solve lot sizing problems discussing their main components such as representation evaluation neighborhood definition and genetic operators further we briefly review other solution approaches such as dynamic programming cutting planes dantzig wolfe decomposition lagrange relaxation and dedicated heuristics this allows us to compare these techniques understanding their respective advantages and disadvantages gives insight into how we can integrate elements from several solution approaches into more powerful hybrid algorithms finally we discuss general guidelines for computational experiments and illustrate these with several examples

reliable facility location design under the risk of disruptions reliable facility location models consider unexpected failures with site dependent probabilities as well as possible customer reassignment this paper proposes a compact mixed integer program mip formulation and a continuum approximation ca model to study the reliable uncapacitated fixed charge location problem rufl which seeks to minimize initial setup costs and expected transportation costs in normal and failure scenarios the mip determines the optimal facility locations as well as the optimal customer assignments and is solved using a custom designed lagrangian relaxation lr algorithm the ca model predicts the total system cost without details about facility locations and customer assignments and it provides a fast heuristic to find near optimum solutions our computational results show that the lr algorithm is efficient for mid sized rufl problems and that the ca solutions are close to optimal in most of the test instances for large scale problems the ca method is a good alternative to the lr algorithm that avoids prohibitively long running times

modeling and solving the two facility capacitated network loading problem this paper studies a topical and economically significant capacitated network design problem that arises in the telecommunications industry in this problem given point to point communication demand in a network must be met by installing loading capacitated facilities on the arcs loading a facility incurs an arc specific and facility dependent cost this paper develops modeling and solution approaches for loading facilities to satisfy the given demand at minimum cost we consider two approaches for solving the underlying mixed integer program a lagrangian relaxation strategy and a cutting plane approach that uses three classes of valid inequalities that we identify for the problem we show that a linear programming formulation that includes these inequalities always approximates the value of the mixed integer program at least as well as the lagrangian relaxation bound our computational results on a set of prototypical telecommunication data show that including these inequalities considerably improves the gap between the integer programming formulation and its linear programming relaxation from an average of 25 to an average of 8 these results show that strong cutting planes can be an effective modeling and algorithmic tool for solving problems of the size that arise in the telecommunications industry

svd based design and new structures for variable fractional delay digital filters this paper shows that the problem of designing one dimensional 1 d variable fractional delay vfd digital filter can be elegantly reduced to the easier subproblems that involve one dimensional 1 d constant filter subfilter designs and 1 d polynomial approximations by utilizing the singular value decomposition svd of the variable design specification we prove that both 1 d constant filters and 1 d polynomials possess either symmetry or anti symmetry simultaneously therefore a vfd filter can be efficiently obtained by designing 1 d constant filters with symmetrical or antisymmetrical coefficients and performing 1 d symmetrical or antisymmetrical approximations to perform the weighted least squares wls vfd filter design a new wls svd method is also developed moreover an objective criterion is proposed for selecting appropriate subfilter orders and polynomial degrees our computer simulations have shown that the svd based design and wls svd design can achieve much higher design accuracy with significantly reduced filter complexity than the existing wls design method another important part of the paper proposes two new structures for efficiently implementing the resulting vfd filter which require less computational complexity than the so called farrow structure

single machine scheduling with symmetric earliness and tardiness penalties abstract this research focuses on scheduling jobs with varying processing times and distinct due dates on a single machine subject to earliness and tardiness penalties hence this work will find application in a just in time jit production environment the scheduling problem is formulated as a 0 1 linear integer program with three sets of constraints where the objective is to minimize the sum of the absolute deviations between job completion times and their respective due dates the first two sets of constraints are equivalent to the supply and demand constraints of an assignment problem the third set which represents the process time non overlap constraints is relaxed to form the lagrangian dual problem the dual problem is then solved using the subgradient algorithm efficient heuristics have also been developed in this work to yield initial primal feasible solutions and to convert primal infeasible solutions to feasibility the computational results show that the relative deviation from optimality obtained by the subgradient algorithm is less than 3 for problem sizes varying from 10 to 100 jobs

3 d depth migration via mcclellan transformations three dimensional seismic wavefields may be extrapolated in depth one frequency at a time by two dimensional convolution with a circularly symmetric frequency and velocity dependent filter this depth extrapolation performed for each frequency independently lies at the heart of 3 d finite difference depth migration the computational efficiency of 3 d depth migration depends directly on the efficiency of this depth extrapolation mcclellan transformations provide an efficient method for both designing and implementing two dimensional digital filters that have a particular form of symmetry such as the circularly symmetric depth extrapolation filters used in 3 d depth migration given the coefficients of one dimensional frequency and velocity dependent filters used to accomplish 2 d depth migration mcclellan transformations lead to a simple and efficient algorithm for 3 d depth migration 3 d depth migration via mcclellan transformations is simple because the coefficients of two dimensional depth

matrix based algorithms for constrained least squares and minimax designs of 2 d linear phase fir filters the impulse response coefficients of a two dimensional 2 d finite impulse response fir filter are in a matrix form in nature conventional optimal design algorithms rearrange the filter s coefficient matrix into a vector and then solve for the coefficient vector using design algorithms for one dimensional 1 d fir filters some recent design algorithms have exploited the matrix nature of the 2 d filter s coefficients but not incorporated with any constraints and thus are not applicable to the design of 2 d filters with explicit magnitude constraints in this paper we develop some efficient algorithms exploiting the coefficients matrix nature for the constrained least squares cls and minimax designs of quadrantally symmetric 2 d linear phase fir filters both of which can be formulated as an optimization problem or converted into a sequence of subproblems with a positive definite quadratic cost and a finite number of linear constraints expressed in terms of the filter s coefficient matrix design examples and comparisons with several existing algorithms demonstrate the effectiveness and efficiency of the proposed algorithms

implementation of 2 d digital filters by iterative methods a two dimensional 2 d rational filter can be implemented by an iterative computation involving only finite extent impulse response fir filtering operations provided a certain convergence criterion is met in this paper we generalize this procedure so that the convergence criterion is satisfied for any stable 2 d rational transfer function one formulation which guarantees convergence invokes a relaxed form of the iterative computation along with prefiltering the numerator and denominator polynomials of the rational transfer function this implementation may be applied with a frequency varying relaxation parameter for increasing the rate of convergence an alternative generalization uses several previously computed iterates unlike our first modification which utilizes only the most recently computed iterate this formulation can potentially guarantee convergence and also increase the convergence rate without the requirement of prefiltering another extension of the iterative computation incorporates constraints e g positivity or finite extent on the output of each iteration proof of convergence of such constrained iterations relies on the concept of a nonexpansive operator in particular the error introduced within the converging solution resulting from a finite extent constraint is shown to satisfy a homogeneous partial difference equation finally this error computation leads to an important link between our iterative implementation with constraints and an iterative solution to partial difference equations e g laplace s equation with known boundary conditions

a novel method for designing fir digital filters with nonuniform frequency samples a new method of designing fir digital filters using nonuniform frequency samples is presented there is no restriction on the phase to be linear the method is based on a newton type polynomial interpolating on the unit circle of the complex plane attractive features of the proposed method are the applicability to unequally spaced samples the recursive and semipermanent computation of filter parameters the capability of obtaining short transition bands or sharp cut off frequency responses and the design of efficient algorithms for real time applications in the serial case when the next sample appears the design parameters are evaluated only by updating the old ones with correction terms that could be used as indicators for convergence approximation or filter reduction the method can be extended to m d filter design dft calculation design of parallel algorithms etc

a new lagrangian relaxation approach to the generalized assignment problem abstract in this paper we present a new lagrangian relaxation approach to the generalized assignment problem gap the new approach is based on a reformulation of gap into an equivalent problem which is then relaxed by traditional lagrangian relaxation techniques the reformulation is created by introducing a set of auxiliary variables and a number of coupling constraints by relaxing the coupling constraints we get subproblems where both types of constraint structures present in the gap are active the lower bound from the lagrangian dual of this approach is shown to be at least as strong as that from the best of the traditional lagrangian relaxation approaches an important feature is also the possibility of generating upper bounds quite easily the new approach has been tested on 10 problems of size m 4 n 25 i e 100 0 1 variables and the results have been compared with the traditional approaches

on the consistency of finite element models in thermoelastic analysis in thermoelastic analysis compatible finite elements may predict oscillating stresses if the temperature distribution is not coherent with the element strain coming from the assumed displacement approximation modelling the stress field as an independent variable could be a viable alternative to avoid these spurious outcomes to this purpose the behavior of mixed hybrid stress and equilibrium finite element models in the presence of initial strains due to temperature is investigated and compared with the usually employed displacement approach the consistency requirement for each model is established and the spurious outcomes due to inconsistent temperature fields are discussed examining also the effects of element geometry distortions the analysis illustrated through some numerical tests shows that a direct approximation for the stress field can eliminate or at least reduce the generation of spurious stress modes although this is not a priori guaranteed by a mixed approach

weighted least mean square design of 2 d fir digital filters the general case this paper solves the weighted least mean square wlms design of two dimensional 2 d finite impulse response fir filters with general half plane symmetric frequency responses and nonnegative weighting functions the optimal solution is characterized by a pair of coupled integral equations and the existence and uniqueness of the wlms solution for 2 d fir filter design are established two efficient numerical algorithms using a 2 d fast fourier transform fft are proposed to solve the wlms solution one is based on the contraction mapping and fix point theorem characterizing the coupled integral equation the other uses conjugate gradient techniques which guarantees finite convergence the associated computational complexity is analyzed and compared with existing algorithms examples are used to illustrate the effectiveness of the proposed design algorithms the selection of weighting functions to improve the minimax performance of the filter is also discussed

generating fenchel cutting planes for knapsack polyhedra the author recently proposed a class of cutting planes for integer programs called fenchel cuts which distinguish themselves from more conventional cuts in that they are generated by directly seeking to solve the separation problem rather than by using explicit knowledge of the polyhedral structure of the integer program an algorithm for generating fenchel cuts is presented and described in detail for the separation problem associated with knapsack polyhedra computational results are presented for a collection of real world integer programs to demonstrate the effectiveness of the cutting planes

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

a 2 d block decomposition technique for designing 2 d fir filters from frequency samples a new technique for computing the coefficients of a class of 2 d polynomials from samples that are located anywhere in the plane or distributed on curves with desired shapes is presented the algorithm is based on a 2 d block decomposition technique suitable for deriving the lu products of the interpolation matrix a variation of this technique leads to an efficient solution of 2 d interpolation problems for which the interpolation points occur in complex conjugate pairs but where the coefficients of the interpolation polynomial are real these results are applied in designing 2 d fir filters the algorithm proposed permits all operations to be performed by real arithmetic guarantees real results saves a number of operations and produces accurate solutions even in case of designing high order 2 d fir filters or when the interpolation matrix is ill conditioned the algorithm is well suited to parallel computations and can be extended to design m d fir digital filters or to invert m d interpolation matrices

the tv break packing problem abstract instead of selling advertisement spots one by one some french satellite channels decided in 2002 to modify their commercial offer in order to sell packages of spots these new general conditions of sale lead to an interesting optimization problem that we named the tv b reak p acking p roblem tvbp we establish its np hardness and study various resolutions approaches including linear programming lp lagrangian relaxation lr constraint programming cp and local search ls finally we propose a generic cp ls hybridization scheme branch and move whose application to the tvbp obtained the best results in our experiments dual upper bounds of the maximal revenue are also computed

new strategy for assumed stresses for 4 node hybrid stress membrane element an oblique skew co ordinate system defined at the origin of the isoparametric co ordinates is introduced as the reference co ordinate system for assumed stresses in the formulation of a 4 node hybrid membrane element the initially uncoupled stresses in these reference co ordinates can be constrained to satisfy the equilibrium conditions pointwise by using the procedure of pian and wu7 when suitable incompatible displacements are introduced such strategy allows the element stiffness to be formulated by using either the hellinger reissner or the complementary energy functional numerical results show that the performances of three elements constructed by using different sets of incompatible displacements in this paper are practically identical and are all of slightly higher accuracy than that of the pian sumihara element6

design of one way wavefield extrapolation operators using smooth functions in wlsq optimization many depth migration methods use one way frequency space depth extrapolation methods these methods are generally considered to be expensive so it is important to find the most efficient way of implementing them this usually means making spatial convolution operators that are as short as possible applying the extrapolation operators in a recursive way using small depth steps also demands that the operators do not amplify the wavefield at every depth step weighted least squares is an appropriate method to use for designing extrapolation operators that are accurate and efficient and that remain stable in a recursive algorithm the extrapolated wavefields calculated with these operators are comparable with the extrapolation results obtained with other known operator design techniques as the remez exchange method and nonlinear optimization in this paper the weighted least squares technique is refined by using different model functions by smoothing the phase and amplitude transition at the evanescent c

relations between incompatible displacement model and hybrid stress model an examination of the variational formulations confirms the similarity between the incompatible displacement model and the assumed stress hybrid model that was pointed out by irons in 1972 but the basic differences between the two are also identified for 8 node solid elements the assumed stress terms obtained through a rational procedure also agree with those deduced by irons purely from his physical insight

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 new technique for the design of two dimensional fir and iir filters the design problem of two dimensional digital filters is the subject of this paper the problem is formulated for both fir and iir filters in such a way that the performance index is a convex function of the optimization vector the design technique is based on newton s method each iteration consists of n easily computed steps where n is the number of parameters to be optimized the coefficients can be obtained in the quantization levels according to the desired number representation illustrative examples and comparisons with existing techniques are also included