a rigorous computational comparison of alternative solution methods for the generalized assignment problem statistical experimental design and analysis is a cornerstone for scientific inquiry that is rarely applied in reporting computational testing this approach is employed to study the relative performance characteristics of the four leading algorithmic and heuristic alternatives to solve the linear cost generalized assignment problem lcgap against a newly developed heuristic variable depth search heuristic vdsh in assessing the relative effectiveness of the prominent solution methodologies and vdsh under the effects of various problem characteristics we devise a carefully designed experimentation of state of the art implementations through a rigorous statistical analysis we identify the most efficient method s for commonly studied lcgaps and determine the effect on solution time and quality of problem class and size

lagrangean decomposition a model yielding stronger lagrangean bounds given a mixed integer programming problem with two matrix constraints it is possible to define a lagrangean relaxation such that the relaxed problem decomposes additively into two subproblems each having one of the two matrices of the original problem as its constraints there is one lagrangean multiplier per variable we prove that the optimal value of this new lagrangean dual dominates the optimal value of the lagrangean dual obtained by relaxing one set of constraints and give a necessary condition for a strict improvement we show on an example that the resulting bound improvement can be substantial we show on a complex practical problem how lagrangean decomposition may help uncover hidden special structures and thus yield better solution methodology

renormalization theory in four dimensional scalar fields i we present a renormalization group approach to the renormalization theory of 44 using techniques that have been introduced and used in previous papers and that lead to very simple methods to bound the coefficients of the effective potential and of the schwinger functions the main aim of this paper is to show how one can in this way obtain then bounds

local existence of the borel transform in euclidean φ 4 4 we bound rigorously the large order behaviour of 44 euclidean perturbative quantum field theory as the simplest example of renormalizable but non super renormalizable theory the needed methods are developed to take into account the structure of renormalization which plays a crucial role in the estimates as a main thorem it is shown that the schwinger functions at ordern are bounded byknn which implies a finite radius of convergence for the borel transform of the perturbation series

a comparison of heuristics and relaxations for the capacitated plant location problem abstract approaches proposed in the literature for the capacitated plant location problem are compared the comparison is based on new theoretical and computational results the main emphasis is on relaxations in particular dominance relations among the various relaxations found in the literature are identified in the computational study the relaxations are compared as a function of various characteristics of the test problems several of these relaxations can be used to generate heuristic feasible solutions that are better than the classical greedy or interchange heuristics both in computing time and in the quality of the solutions found

dimensional regularization and renormalization of qed we give an space definition of dimensional regularization suited to the tree expansion method of renormalization we apply the dimensionally regularized tree expansion to qed obtaining sharp bounds on the size of a renormalized graph subtractions are made with the lagrangian counterterms of the tree expansion not by minimal subtraction techniques and so do not entail a knowledge of the meromorphic structure of a graph as a function of dimension this renormalization procedure respects the ward identities and the counterterms required are gauge invariant

constrained multi project plannings problems a lagrangean decomposition approach abstract this paper describes a lagragean decomposition technique for solving multi project planning problems with resource constraints and alternative modes of performing each activity in the projects the decompsition can be useful in several ways from one side it provides bounds on the optimum so that the quality of approximate solutions can be evaluated furthermore in the context of branch and bound algorithms it can be used for more effective fathoming of the tree nodes finally in the modelling perspective the la grangean optimal multipliers can provide insights to project managers as prices for assigning the resources to different projects

a renormalization group proof of perturbative renormalizability this paper presents a proof of bounds on the renormalized perturbation expansion of the euclidean 4 4 theory its aim is partly pedagogical by combining the insights and techniques of numerous authors it is now possible to define the perturbation expansion and bound it in a very few pages the present version is based on the renormalized tree expansion adapted to the continuous renormalization group all detailed results are proved by induction on the size of the tree the continuous rg version presented here has one big advantage over the discrete rg version discussed elsewhere in the continuous version a tree has a more restrictive structure there is a one to one correspondence between forks of the tree and lines of feynman graphs this extra structure eliminates the need to introduce feynman graphs in the first place it also reduces the number of cases to be analyzed at a given inductive step and simplifies the combinatorical estimates

on nonsingular sign regular matrices abstract an m n matrix a is sign regular if for each k 1 k min m n all k k submatrices of a have determinant with the same nonstrict sign the zero pattern of nonsingular sign regular matrices is analyzed it is proved that the number of zero entries which can appear in a nonsingular sign regular matrix depends on its signature a matrix is totally nonpositive if all its minors are nonpositive a test for recognizing nonsingular totally nonpositive matrices is also provided

notes on hilbert and cauchy matrices inspired by examples of small hilbert matrices the author proves a property of symmetric totally positive cauchy matrices called at property and consequences for the hilbert matrix

combined matrices of almost strictly sign regular matrices abstract the combined matrix is a very useful concept for many applications almost strictly sign regular assr matrices form an important structured class of matrices with two possible zero patterns which are either type i staircase or type ii staircase we prove that under an irreducibility condition the pattern of zero and nonzero entries of an assr matrix is preserved by the corresponding combined matrix without the irreducibility condition it is proved that type i and type ii staircases are still preserved illustrative numerical examples are included

bounds on renormalized feynman graphs we prove two bounds on the value of renormalized euclidean feynman graphs one is a relatively crude but widely applicable bound the other a finer bound applicable to 4 4 like models

running coupling expansion for the renormalized φ 4 4 trajectory from renormalization invariance we formulate a renormalized running coupling expansion for the function and the potential of the renormalized 4 trajectory on four dimensional euclidean space time renormalization invariance is used as a first principle no reference is made to bare quantities the expansion is proved to be finite to all orders of perturbation theory the proof includes a large momentum bound on the connected free propagator amputated vertices

combined matrices in special classes of matrices abstract the combined matrix of a nonsingular matrix a is the matrix a a 1 t where means the hadamard entrywise product it has simple properties its row as well as column sums are always one and it is not changed if a is multiplied from either side by a nonsingular diagonal matrix although it is usually difficult to compute its further properties deserve attention in the paper we concentrate on the sequence of the diagonal entries of combined matrices in various classes of matrices

a survey of algorithms for the generalized assignment problem abstract this paper surveys algorithms for the well known problem of finding the minimum cost assignment of jobs to agents so that each job is assigned exactly once and agents are not overloaded all approaches seem to be based on branch and bound with bound supplied through heuristics and through relaxations of the primal problem formulation from the survey one can select building blocks for the design of one s own tailor made algorithm the survey also reveals that although just about every mathematical programming technique was tried on this problem there is still a lack of a representative set of test problems on which competing enumeration algorithms can be compared as well as a shortage of effective heuristics

some applications of doubly stochastic matrices abstract we discuss primarily two applications of doubly stochastic matrices and related matrices the first concerns a topic in communication theory called satellite switched time division multiple access systems and we attempt to illuminate some results which have occured in the engineering literature the second concerns a recent notion of a doubly stochastic automorphism of a graph we prove several new theorems about doubly stochastic automorphisms of certain classes of graphs and in particular obtain a theorem of which birkhoff s theorem for doubly stochastic matrices is a special case

construction and borel summability of infrared φ 4 4 by a phase space expansion we construct the thermodynamic limit of the critical massless 4 model in 4 dimensions with an ultraviolet cutoff by means of a partly renormalized phase space expansion this expansion requires in a natural way the introduction of effective or running constants and the infrared asymptotic freedom of the model i e the decay of the running coupling constant plays a crucial role we prove also that the correlation functions of the model are the borel sums of their perturbation expansion

maximal covering code multiplexing access telecommunication networks abstract we present a maximal covering model for the network design of code division multiplexing access cdma telecommunication system properties of the solution and the algorithm have been studied the model has been developed to solve actual problems they are extremely large so exact decomposition methods cannot be used to solve it a lagrangian decomposition heuristic has been defined different algorithm options have been computationally compared using random generated and actual data model and algorithm parameters have been adjusted and sensibility of the solution to the data has been considered in these tests

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

combined matrices of sign regular matrices abstract the combined matrix of a nonsingular matrix a is the hadamard entry wise product c a a a 1 t since each row and column sum of c a is equal to one the combined matrix is doubly stochastic when it is nonnegative in this work we study the nonnegativity of the combined matrix of sign regular matrices based upon their signature in particular a few coordinates of the signature e of a play a crucial role in determining whether or not c a is nonnegative

nonsingular almost strictly sign regular matrices abstract the class of nonsingular almost strictly totally positive matrices has been characterized m gasca j m pena characterizations and decompositions of almost strictly positive matrices siam j matrix anal appl 28 2006 1 8 in this paper we discuss the class of almost strictly sign regular matrices that includes almost strictly totally positive matrices a characterization is provided for these matrices in terms of their nontrivial minors using consecutive rows and consecutive columns in particular we present a characterization of certain almost strictly sign regular matrices in terms of a very reduced number of boundary almost trivial minors

perturbative renormalization of composite operators via flow equations i we apply the general framework of the continuous renormalization group whose significance for perturbative quantum field theories was recognized by polchinski to investigate by new and mathematically simple methods the perturbative renormalization of composite operators in this paper we demonstrate the perturbative renormalizability of the green functions of the euclidean massive 44 theory with one insertion of a possibly oversubtracted in the bphz language composite operator moreover we show that our method admits an easy proof of the zimmermann identities and of the lowenstein rule

an algebraic birkhoff decomposition for the continuous renormalization group this paper aims at presenting the first steps towards a formulation of the exact renormalization group equation in the hopf algebra setting of connes and kreimer it mostly deals with some algebraic preliminaries allowing us to formulate perturbative renormalization within the theory of differential equations the relation between renormalization formulated as a change of boundary condition for a differential equation and an algebraic birkhoff decomposition for rooted trees is explicited

a renormalizable field theory the massive gross neveu model in two dimensions the euclidean massive gross neveu model in two dimensions is just renormalizable and asymptotically free thanks to the pauli principle bare perturbation theory with an ultra violet cut off and the correct ansatz for the bare mass is convergent in a disk whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant therefore the theory can be fully constructed in a perturbative way it satisfies the o s axioms and is the borel sum of the renormalized perturbation expansion of the model