on the hadamard formula for nonsmooth domains we consider the first eigenvalue of the dirichlet laplacian in three cases c1 1 domains lipschitz domains and bounded domains without any smoothness assumptions asymptotic formula for this eig

uniform concentration compactness for sobolev spaces on variable domains abstract we present a new method for proving existence results in shape optimization problems involving the eigenvalues of the dirichlet laplace operator this method brings together the convergence theory and the concentration compactness principle given a sequence of open sets a n n n in r n not necessarily bounded but of uniformly bounded measure we prove a concentration compactness result in l l 2 r n for the sequence of resolvent operators r a n n n where r a n l 2 r n h 1 0 a n r a n 1

on the sharp effect of attaching a thin handle on the spectral rate of convergence abstract consider two domains connected by a thin tube it can be shown that the resolvent of the dirichlet laplacian is continuous with respect to the channel section parameter this in particular implies the continuity of isolated simple eigenvalues and the corresponding eigenfunctions with respect to domain perturbation under an explicit nondegeneracy condition we improve this information providing a sharp control of the rate of convergence of the eigenvalues and eigenfunctions in the perturbed domain to the relative eigenvalue and eigenfunction in the limit domain as an application we prove that again under an explicit nondegeneracy condition the case of resonant domains features polynomial splitting of the two eigenvalues and a clear bifurcation of eigenfunctions

a heuristic solution for fuzzy mixed model line balancing problem abstract this paper addresses the mixed model line balancing problem with fuzzy processing time a fuzzy binary linear programming model is formulated for the problem this fuzzy model is then transformed to a mixed zero one program due to the complexity nature in handling fuzzy computation new approximated fuzzy arithmetic operation is presented a fuzzy heuristic is developed to solve this problem based on the aggregating fuzzy numbers and combined precedence constraints the general idea of our approach is to arrange the jobs in a sequence by a varying section exchange procedure then jobs are allocated into workstations based on these aggregated fuzzy times with the considerations of technological constraint and cycle time limit promising results are obtained by experiments

the bin packing problem with precedence constraints given a set of identical capacitated bins a set of weighted items and a set of precedences among such items we are interested in determining the minimum number of bins that can accommodate all items and can be ordered in such a way that all precedences are satisfied the problem denoted as the bin packing problem with precedence constraints bpp p has a very intriguing combinatorial structure and models many assembly and scheduling issues according to our knowledge the bpp p has received little attention in the literature and in this paper we address it for the first time with exact solution methods in particular we develop reduction criteria a large set of lower bounds a variable neighborhood search upper bounding technique and a branch and bound algorithm we show the effectiveness of the proposed algorithms by means of extensive computational tests on benchmark instances and comparison with standard integer linear programming techniques

a survey of exact algorithms for the simple assembly line balancing problem in this survey paper we discuss the development of the simple assembly line balancing problem salbp modifications and generalizations over time present alternate 0 1 programming formulations and a general integer programming formulation of the problem discuss other well known problems related to salbp describe and comment on a number of exact i e optimum seeking methods and present a summary of the reported computational experiences all models discussed here are deterministic i e all input parameters are assumed to be known with certainty and all the algorithms discussed are exact the problem is termed simple in the sense that no mixed models subassembly lines zoning restrictions etc are considered due to the richness of the literature we exclude from discussion here a the inexact i e heuristic approximate algorithms for salpb and b the algorithms for the general assembly line balancing problem including the stochastic models

the c r dependence problem of eigenvalues of the laplace operator on domains in the plane abstract the c r dependence problem of multiple dirichlet eigenvalues on domains is discussed for elliptic operators by regarding c r 1 smooth one parameter families of c 1 perturbations of domains in r n as applications of our main theorem theorem 1 we provide a fairly complete description for all eigenvalues of the laplace operator on disks and squares in r 2 and also for its second eigenvalue on balls in r n for any n 3 the central tool used in our proof is a degenerate implicit function theorem on banach spaces theorem 2 of independent interest

geometrically induced phase transitions in two dimensional dumbbell shaped domains abstract we continue the analysis started in 23 of a two dimensional non convex variational problem motivated by studies on magnetic domain walls trapped by thin necks the main focus is on the impact of extreme geometry on the structure of local minimizers representing the transition between two different constant phases we address here the case of general non symmetric dumbbell shaped domains with a small constriction and general multi well potentials our main results concern the existence and uniqueness of non constant local minimizers their full classification in the case of convex bulks and the complete description of their asymptotic behavior as the size of the constriction tends to zero

capacite et inegalite de faber krahn dans rn abstract in this paper we define a new capacity which allows us to control the behaviour of the dirichlet spectrum of a compact riemannian manifold with boundary with small subsets which may intersect the boundary removed this result generalises a classical result of rauch and taylor the crushed ice theorem in the second part we show that the dirichlet spectrum of a sequence of bounded euclidean domains converges to the spectrum of a ball with the same volume if the first eigenvalue of these domains converges to the first eigenvalue of a ball

a faber krahn inequality for robin problems in any space dimension we prove a faber krahn inequality for the first eigenvalue of the laplacian with robin boundary conditions asserting that amongst all lipschitz domains of fixed volume the ball has the smallest first eigenvalue we prove the result in all space dimensions using ideas from m h bossel c r acad sci paris ser i math 302 1986 47 50 where a proof for smooth domains in the plane was given the method does not involve the use of symmetrisation arguments the results also imply variants of the cheeger inequality for the first eigenvalue

a linear programming approach for linear programs with probabilistic constraints we study a class of mixed integer programs for solving linear programs with joint probabilistic constraints from random right hand side vectors with finite distributions we present greedy and dual heuristic algorithms that construct and solve a sequence of linear programs we provide optimality gaps for our heuristic solutions via the linear programming relaxation of the extended mixed integer formulation of luedtke et al 2010 13 as well as via lower bounds produced by their cutting plane method while we demonstrate through an extensive computational study the effectiveness and scalability of our heuristics we also prove that the theoretical worst case solution quality for these algorithms is arbitrarily far from optimal our computational study compares our heuristics against both the extended mixed integer programming formulation and the cutting plane method of luedtke et al 2010 13 our heuristics efficiently and consistently produce solutions with small optimality gaps while for larger instances the extended formulation becomes intractable and the optimality gaps from the cutting plane method increase to over 5

second order conic approximation for disassembly line design with joint probabilistic constraints a problem of profit oriented disassembly line design and balancing with possible partial disassembly and presence of hazardous parts is studied the objective is to design a production line providing a maximal revenue with balanced workload task times are assumed to be random variables with known normal probability distributions the cycle time constraints are to be jointly satisfied with at least a predetermined probability level an and or graph is used to model the precedence relationships among tasks several lower and upper bounding schemes are developed using second order cone programming and convex piecewise linear approximation to show the relevance and applicability of the proposed approach a set of instances from the literature are solved to optimality

uniformity and the taylor expansion of ordinary lambda terms we define the complete taylor expansion of an ordinary lambda term as an infinite linear combination with rational coefficients of terms of a resource calculus similar to boudol s lambda calculus with multiplicities or with resources in our resource calculus all applications are multi linear in the algebraic sense i e commute with linear combinations of the function or the argument we study the collective behaviour of the beta reducts of the terms occurring in the taylor expansion of any ordinary lambda term using in a surprisingly crucial way a uniformity property that they enjoy as a corollary we obtain the main part of a proof that this taylor expansion commutes with bohm tree computation syntactically

the nodal line of the second eigenfunction of the robin laplacian in r2 can be closed abstract we construct a multiply connected domain in r 2 for which the second eigenfunction of the laplacian with robin boundary conditions has an interior nodal line in the process we adapt a bound of donnelly fefferman type to obtain a uniform estimate on the size of the nodal sets of a sequence of solutions to a certain class of elliptic equations in the interior of a sequence of domains which does not depend directly on any boundary behaviour this also gives a new proof of the nodal line property of the example in the dirichlet case

genetic algorithm based technique for solving chance constrained problems management and measurement of risk is an important issue in almost all areas that require decisions to be made under uncertain information chance constrained programming ccp have been used for modelling and analysis of risks in a number of application domains however the resulting mathematical problems are non trivial to represent using algebraic modelling languages and pose significant computational challenges due to their non linear non convex and the stochastic nature we develop and implement c classes to represent such ccp problems we propose a framework consisting of genetic algorithm and monte carlo simulation in order to process the problems the non linear and non convex nature of the ccp problems are processed using genetic algorithm whereas the stochastic nature is addressed through simulation the computational investigations have shown that the framework can efficiently represent and obtain good solutions for seven test problems

probabilistic analysis of bin packing heuristics in this paper we present both a probabilistic and statistical analysis of several bin packing heuristics with mild conditions on the distribution of problem data we show that the ratio of the expected number of bins packed for these heuristics to the number of elements converges to some constant this constant can either be derived analytically or estimated through simulation we analyze the variance in performance of these heuristics and we further show that as the number of elements n increases the probability that the number of bins required for these heuristics exceeds any fixed percentage of their expected performance goes to zero

a semantic measure of the execution time in linear logic we give a semantic account of the execution time i e the number of cut elimination steps leading to the normal form of an untyped mell net we first prove that 1 a net is head normalizable i e normalizable at depth 0 if and only if its interpretation in the multiset based relational semantics is not empty and 2 a net is normalizable if and only if its exhaustive interpretation a suitable restriction of its interpretation is not empty we then give a semantic measure of execution time we prove that we can compute the number of cut elimination steps leading to a cut free normal form of the net obtained by connecting two cut free nets by means of a cut link from the interpretations of the two cut free nets these results are inspired by similar ones obtained by the first author for the untyped lambda calculus

a simulated annealing algorithm with the random compound move for the sequential partitioning problem of directed acyclic graphs abstract in this paper we present an approach for finding a minimum cost partition of the nodes of a directed acyclic graph into subsets of a given size subject to the constraint that the precedence relationships among the elements are satisfied based on the concept of simulated annealing simulated annealing is generally applicable and can be used to obtain solutions arbitrarily close to an optimum however the standard simulated annealing approach with a conventional neighbourhood structure does not yield good solutions for this problem since this is a multiple partitioning problem and the number of subsets is not fixed for this problem we develop an effective neighbourhood structure and a new acceptance criterion we also assess the effectiveness of the developed algorithm the results show that this proposed algorithm outperforms in terms of solution quality any other algorithm using tabu search the computational time of the procedure is proportional to the number of nodes in the graph

an optimal piecewise linear program for the u line balancing problem with stochastic task times abstract the utilization of u shaped layouts in place of the traditional straight line configuration has become increasingly popular with reported benefits of substantial improvements in productivity and quality this paper examines the u line balancing problem with stochastic task times a chance constrained piecewise linear integer program is formulated to find the optimal solution various approaches used to identify a tight lower bound are also presented as are operable extensions to the basic model computational results show that the proposed method is able to solve practical sized problems

maximizing the production rate in simple assembly line balancing a branch and bound procedure abstract in this paper a branch and bound procedure for the simple assembly line balancing problem type 2 salbp 2 is described this np hard problem consists of assigning tasks to a given number of work stations of a paced assembly line so that the production rate is maximized besides possible precedence constraints between the tasks have to be considered existing solution procedures for salbp 2 are mainly based on repeatedly solving instances of the closely related salbp 1 which is to minimize the number of stations for a given production rate the proposed branch and bound procedure directly solves salbp 2 by using a new enumeration technique the local lower bound method which is complemented by a number of bounding and dominance rules computational results indicate that the new procedure is very efficient

a nonlinear parabolic equation with varying domain abstract this document considers a boundary value problem where the basic problem is to understand how new equilibrium solutions may appear for a given nonlinear function f as the domain omega is changed these new solutions being bifurcations from known equilibrium solutions for a given cubic function f an intuitive discussion of this phenomenon was given by hale indicating how stable non constant equilibria appear as secondary rather than primary bifurcations additional keywords continuity perturbations reprints

a joint chance constrained programming model with row dependence abstract joint chance constrained stochastic programming models typically require random row vector independence a joint model is developed that incorporates not only within constraint covariance as is usually the case but also admits dependence between constraints that is row dependence the objective function of the associated chance constrained deterministic equivalent is a multivariate normal distribution with dimension equal to the number of chance constraints in the original problem we discuss methods to solve this multinormal integral and evaluate its derivatives the model is implemented in portable fortran and applied to two 9 d test problems

velocity extension for the level set method and multiple eigenvalues in shape optimization in the context of structural optimization by the level set method we propose an extension of the velocity of the underlying hamilton jacobi equation the gradient method is endowed with a hilbertian structure based on the h1 sobolev space numerical results for compliance minimization and mechanism design show a strong improvement of the rate of convergence of the level set method another important application is the optimization of multiple eigenvalues

branch and bound algorithms for the multi product assembly line balancing problem abstract this paper considers a flexible manufacturing system for several products each requiring a number of sequential nonpreemptive tasks some of which may be common to many products work stations are capable of handling any task the objective is to minimize the number of work stations necessary to manufacture all products so that tasks are performed in the proper order and so that all tasks assigned to any given station can be executed within a prescribed time frame a new branch and bound approach for this problem is presented it contains two main improvements over previously published tree search algorithms an improved lower bounding procedure and a more powerful partitioning scheme the algorithm can be used either as a heuristic in its truncated version or as an exact method in its full version tests performed on randomly generated problems confirm the effectiveness of the proposed improvements

spectral stability of dirichlet second order uniformly elliptic operators we prove sharp stability results for the dependence of the eigenvalues of second order uniformly elliptic linear operators with homogeneous dirichlet boundary conditions upon domain perturbation

dirichlet problems on varying domains abstract the aim of the paper is to characterise sequences of domains for which solutions to an elliptic equation with dirichlet boundary conditions converge to a solution of the corresponding problem on a limit domain necessary and sufficient conditions are discussed for strong and uniform convergence for the corresponding resolvent operators examples are given to illustrate that most results are optimal

balancing stochastic two sided assembly lines a chance constrained piecewise linear mixed integer program and a simulated annealing algorithm abstract two sided assembly lines are often designed to produce large sized products such as automobiles trucks and buses in this type of a production line both left side and right side of the line are used in parallel in all studies on two sided assembly lines the task times are assumed to be deterministic however in real life applications especially in manual assembly lines the tasks may have varying execution times defined as a probability distribution the task time variation may result from machine breakdowns loss of motivation lack of training non qualified operators complex tasks environment etc in this paper the problem of balancing two sided assembly lines with stochastic task times stalbp is considered a chance constrained piecewise linear mixed integer program cpmip is proposed to model and solve the problem as a solution approach a simulated annealing sa algorithm is proposed to assess the effectiveness of cpmip and sa algorithm a set of test problems are solved finally computational results indicating the effectiveness of cpmip and sa algorithm are reported

on safe tractable approximations of chance constraints abstract a natural way to handle optimization problem with data affected by stochastic uncertainty is to pass to a chance constrained version of the problem where candidate solutions should satisfy the randomly perturbed constraints with probability at least 1 while being attractive from modeling viewpoint chance constrained problems as they are are in general computationally intractable in this survey paper we overview several simulation based and simulation free computationally tractable approximations of chance constrained convex programs primarily those of chance constrained linear conic quadratic and semidefinite programming

singularity of eigenfunctions at the junction of shrinking tubes part ii abstract consider two domains connected by a thin tube it can be shown that generically the mass of a given eigenfunction of the dirichlet laplacian concentrates in only one of them the restriction to the other domain when suitably normalized develops a singularity at the junction of the tube as the channel section tends to zero our main result states that under a nondegeneracy condition the normalized limiting profile has a singularity of order n 1 where n is the space dimension we give a precise description of the asymptotic behavior of eigenfunctions at the singular junction which provides us with some important information about its sign near the tunnel entrance more precisely the solution is shown to be one sign in a neighborhood of the singular junction in other words we prove that the nodal set does not enter inside the channel

bounds for assembly line balancing heuristics we analyze the asymptotic worst case performance ratio of polynomial time heuristics for the assembly line balancing problem assuming that p np we show that no polynomial heuristic has worst case ratio less than 1 5 this ratio is known to be not worse than 2 for any reasonable heuristic tighter results are established for problems with only short tasks i e when all processing times do not exceed a given fraction of the cycle time these results apply even to planar series parallel precedence constraints and contrast with known results for situations with an empty precedence relation i e the bin packing problem in particular if p np there are no fully polynomial approximation schemes for assembly line balancing even with short tasks and planar series parallel precedence constraints

workforce planning in mixed model assembly systems serial assembly systems are formed by arranging several production cells or stations in series we study a popular class of serial assembly lines where all stations have the same production cycle we address a workforce planning problem for such lines which finds applications in labor intensive operations in automobile fire engine aircraft and pc board assembly the problem presented can be applied to lines that produce several variations of a basic stable design i e mixed model transfer lines given a set of n jobs we want to find a sequence that minimizes the maximum workforce requirements over all production cycles an optimal polynomial algorithm for the two station line is presented and the three station case is proved to be strongly x1d4a9 x1d4ab complete several heuristic algorithms that produce upper and lower bounds are developed for the general problem worst case behavior of the upper bounds as well as average performance of lower and upper bounds are reported computational results show that s

spectral theory for perturbed krein laplacians in nonsmooth domains abstract we study spectral properties for h k the krein von neumann extension of the perturbed laplacian v defined on c 0 where v is measurable bounded and nonnegative in a bounded open set r n belonging to a class of nonsmooth domains which contains all convex domains along with all domains of class c 1 r r 1 2 in particular in the aforementioned context we establish the weyl asymptotic formula j n k j 2 n v n n 2 o n 1 2 2 as where v n n 2 n 2 1 denotes the volume of the unit ball in r n and k j j n are the non zero eigenvalues of h k listed in increasing order according to their multiplicities we prove this formula by showing that the perturbed krein laplacian i e the krein von neumann extension of v defined on c 0 is spectrally equivalent to the buckling of a clamped plate problem and using an abstract result of kozlov from the mid 1980s our work builds on that of grubb in the early 1980s who has considered similar issues for elliptic operators in smooth domains and shows that the question posed by alonso and simon in 1980 pertaining to the validity of the above weyl asymptotic formula continues to have an affirmative answer in this nonsmooth setting we also study certain exterior type domains r n k n 3 with k r n compact and vanishing bessel capacity b 2 2 k 0 to prove equality of friedrichs and krein laplacians in l 2 d n x that is c 0 has a unique nonnegative self adjoint extension in l 2 d n x

absalom balancing assembly lines with assignment restrictions abstract assembly line balancing problems albps arise whenever an assembly line is configured redesigned or adjusted an albp consists of distributing the total workload for manufacturing products among the work stations along the line on the one hand research has focussed on developing effective and fast solution methods for exactly solving the simple assembly line balancing problem salbp on the other hand a number of real world extensions of salbp have been introduced but solved with straight forward and simple heuristics in many cases therefore there is a lack of procedures for exactly solving such generalized albp in this paper we show how to extend the well known solution procedure s alome scholl a klein r 1997 s alome a bidirectional branch and bound procedure for assembly line balancing informs j comput 9 319 334 which is able to solve even large salbp instances in a very effective manner to a problem extension with different types of assignment restrictions called aralbp the extended procedure referred to as a bsalom employs a favorable branching scheme an arsenal of bounding rules and a variety of logical tests using ideas from constraint programming computational experiments show that a bsalom is a very promising exact solution approach although the additional assignment restrictions complicate the problem considerably and necessitate a relaxation of some components of s alome

a semantic account of strong normalization in linear logic abstract we prove that given two cut free nets of linear logic by means of their relational interpretations one can determine 1 whether or not the net obtained by cutting the two nets is strongly normalizable 2 in case it is strongly normalizable the maximum length of the reduction sequences starting from that net as a by product of our semantic approach we obtain a new proof of the conservation theorem for multiplicative exponential linear logic mell which does not rely on confluence this yields an alternative proof of strong normalization for mell

note optimal balancing of u shaped assembly lines this note presents an integer programming formulation for determining the optimal balance for the u line line balancing problem it is shown that this model can optimally solve larger problems than previously reported

stability analysis of an optimal balance for an assembly line with fixed cycle time abstract we address the simple assembly line balancing problem minimize the number of stations m for processing n partially ordered operations v 1 2 n within the cycle time c the processing time ti of operation i v and cycle time c are given however during the life cycle of the assembly line the values ti are definitely fixed only for the subset of automated operations v v another subset v v includes manual operations for which it is impossible to fix the exact processing times during the whole life cycle of the assembly line if j v then operation time tj can be different for different cycles of production process for the optimal line balance b of a paced assembly line with vector t t1 t2 tn of the operation times we investigate stability of its optimality with respect to possible variations of the processing times tj of the manual operations j v in particular we derive necessary and sufficient conditions when optimality of the line balance b is stable with respect to sufficiently small variations of the operation times tj j v we show how to calculate the maximal value of independent variations of the processing times of all the manual operations which definitely keep the feasibility and optimality of the line balance b

the generalized gradient at a multiple eigenvalue abstract when a symmetric positive isomorphism between a reflexive banach space that is densely and compactly embedded in a hilbert space and its dual varies smoothly over a banach space its eigenvalues vary in a lipschitz manner we calculate the generalized gradient of the extreme eigenvalues at an arbitrary crossing we apply this to the generalized gradient with respect to a coefficient in an elliptic operator of i the gap between the operator s first two eigenvalues and ii the distance from a prescribed value to the spectrum of the operator

domain dependence of eigenvalues of elliptic type operators the dependence on the domain for the dirichlet eigenvalues of elliptic operators considered in bounded domains is studied the proximity of domains is measured by a norm of the difference of two orthogonal projectors corresponding to the reference domain and the perturbed one this allows to compare eigenvalues corresponding to domains that have non smooth boundaries and different topology the main result is an asymptotic formula in which the remainder is evaluated in terms of this quantity applications of this result are given the results are new for the laplace operator

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

a two process implicit enumeration algorithm for the simple assembly line balancing problem abstract we present an implicit enumeration algorithm for the simple assembly line balancing problem with the objective of minimizing the number of stations along the line for a fixed cycle time the algorithm traverses two branch and bound trees one assigning tasks that appear earlier in the precedence network at lower levels of the tree the other assigning later tasks at lower levels the two processes alternately expand nodes of their respective trees and share information about each other s progress in the form of global bounds computational results are reported on several well known problems from the literature

strong normalization property for second order linear logic the paper contains the first complete proof of strong normalization sn for full second order linear logic ll girard s original proof uses a standardization theorem which is not proven we introduce sliced pure structures sps a very general version of girard s proof nets and we apply to sps gandy s method to infer sn from weak normalization wn we prove a standardization theorem for sps if wn without erasing steps holds for an sps then it enjoys sn a key step in our proof of standardization is a confluence theorem for sps obtained by using only a very weak form of correctness namely acyclicity slice by slice we conclude by showing how standardization for sps allows to prove sn of ll using as usual girard s reducibility candidates

second order cone programming second order cone programming socp problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the cartesian product of second order lorentz cones linear programs convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as socp problems as can many other problems that do not fall into these three categories these latter problems model applications from a broad range of fields from engineering control and finance to robust optimization and combinatorial optimization on the other hand semidefinite programming sdp that is the optimization problem over the intersection of an affine set and the cone of positive semidefinite matrices includes socp as a special case therefore socp falls between linear lp and quadratic qp programming and sdp like lp qp and sdp problems socp problems can be solved in polynomial time by interior point methods the computational effort per iteration required by these methods to solve socp problems is greater than that required to solve lp and qp problems but less than that required to solve sdp s of similar size and structure because the set of feasible solutions for an socp problem is not polyhedral as it is for lp and qp problems it is not readily apparent how to develop a simplex or simplex like method for socp while socp problems can be solved as sdp problems doing so is not advisable both on numerical grounds and computational complexity concerns for instance many of the problems presented in the survey paper of vandenberghe and boyd vb96 as examples of sdps can in fact be formulated as socps and should be solved as such in 2 3 below we give socp formulations for four of these examples the convex quadratically constrained quadratic programming qcqp problem problems involving fractional quadratic functions rutcor rutgers university e mail alizadeh rutcor rutgers edu research supported in part by the u s national science foundation grant ccr 9901991 ieor columbia university e mail gold ieor columbia edu research supported in part by the department of energy grant de fg02 92er25126 national science foundation grants dms 94 14438 cda 97 26385 and dms 01 04282

characterization for the kuratowski limits of a sequence of sobolev spaces the purpose of this paper is to study the strong lower and the weak upper limits in the sense of kuratowski of a sequence of sobolev spaces w1 p0 n n nand compare them to a fixed spacew1 p0 the results are expressed in terms of the behavior of the local capacity in balls of the complementary sets if these two limits coeincide we obtain necessary and sufficient conditions for the convergence in the sense of mosco of the sobolev spaces hence for the continuity of the solution of a dirichlet problem associated to thep laplacian in terms of the geometric domain variation

perturbation of semi linear evolution equations under weak assumptions at initial time abstract we prove perturbation results for abstract semi linear evolution equations in a banach space the main feature is that only very weak assumptions are needed at initial time this allows to prove weak continuity properties and to deal with rather general domain perturbation problems for semi linear parabolic and hyperbolic boundary value problems with various boundary conditions the theory also implies the well known theory on parameter dependent equations

expectation and chance constrained models and algorithms for insuring critical paths in this paper we consider a class of two stage stochastic optimization problems arising in the protection of vital arcs in a critical path network a project is completed after a series of dependent tasks are all finished we analyze a problem in which task finishing times are uncertain but can be insured a priori to mitigate potential delays a decision maker must trade off costs incurred in insuring arcs with expected penalties associated with late project completion times where lateness penalties are assumed to be lower semicontinuous nondecreasing functions of completion time we provide decomposition strategies to solve this problem with respect to either convex or nonconvex penalty functions in particular for the nonconvex penalty case we employ the reformulation linearization technique to make the problem amenable to solution via benders decomposition we also consider a chance constrained version of this problem in which the probability of completing a project on time is sufficiently large we demonstrate the computational efficacy of our approach by testing a set of size and complexity diversified problems using the sample average approximation method to guide our scenario generation

invariant manifolds for parabolic equations under perturbation of the domain abstract we study the effect of domain perturbation on invariant manifolds for semilinear parabolic equations subject to the dirichlet boundary condition under the mosco convergence assumption on the domains we prove the upper and lower semicontinuity of both the local unstable invariant manifold and the local stable invariant manifold near a hyperbolic equilibrium the continuity results are obtained by keeping track of the construction of invariant manifolds in p w bates c k r t jones invariant manifolds for semilinear partial differential equations in dynamics reported vol 2 in dynam report ser dynam systems appl vol 2 wiley chichester 1989 pp 1 38

layer potential techniques in spectral analysis part i complete asymptotic expansions for eigenvalues of the laplacian in domains with small inclusions we provide a rigorous derivation of new complete asymptotic expansions for eigenvalues of the laplacian in domains with small inclusions the inclusions somewhat apart from or nearly touching the boundary are of arbitrary shape and arbitrary conductivity contrast vis a vis the background domain with the limiting perfectly conducting inclusion by integral equations we reduce this problem to the study of the characteristic values of integral operators in the complex plane powerful techniques from the theory of meromorphic operator valued functions and careful asymptotic analysis of integral kernels are combined for deriving complete asymptotic expansions for eigenvalues our asymptotic formulae in this paper may be expected to lead to efficient algorithms not only for solving shape optimization problems for laplacian eigenvalues but also for determining specific internal features of an object based on scattering data measurements

convex approximations of chance constrained programs we consider a chance constrained problem where one seeks to minimize a convex objective over solutions satisfying with a given close to one probability a system of randomly perturbed convex constraints this problem may happen to be computationally intractable our goal is to build its computationally tractable approximation i e an efficiently solvable deterministic optimization program with the feasible set contained in the chance constrained problem we construct a general class of such convex conservative approximations of the corresponding chance constrained problem moreover under the assumptions that the constraints are affine in the perturbations and the entries in the perturbation vector are independent of each other random variables we build a large deviation type approximation referred to as bernstein approximation of the chance constrained problem this approximation is convex and efficiently solvable we propose a simulation based scheme for bounding the optimal value in the chance constrained problem and report numerical experiments aimed at comparing the bernstein and well known scenario approximation approaches finally we extend our construction to the case of ambiguous chance constrained problems where the random perturbations are independent with the collection of distributions known to belong to a given convex compact set rather than to be known exactly while the chance constraint should be satisfied for every distribution given by this set

local and global uniform convergence for elliptic problems on varying domains abstract the aim of the paper is to prove optimal results on local and global uniform convergence of solutions to elliptic equations with dirichlet boundary conditions on varying domains we assume that the limit domain be stable in the sense of keldys amer math soc transl 51 1966 1 73 we further assume that the approaching domains satisfy a necessary condition in the inside of the limit domain and only require l 2 convergence outside as a consequence uniform and l 2 convergence are the same in the trivial case of homogenisation of a perforated domain we are also able to deal with certain cracking domains

the stability radius of an optimal line balance with maximum efficiency for a simple assembly line abstract we consider a simple assembly line balancing problem in which each element of the partially ordered set of assembly operations must be assigned to one element of the set of workstations used for processing the operations an objective is minimizing the product of the number of workstations used in the line balance and the cycle time of the line balance among all admissible line balances an admissible line balance is a partition of all assembly operations into at least two workstations without violating the precedence relations among the assembly operations we assume that during the lifespan of the assembly line the duration of each manual operation may deviate from an initially estimated value while the duration of each automated operation is deterministic we conduct the stability analysis of an optimal line balance first we derive a sufficient and necessary condition for an optimal line balance to be stable second we show that the stability radius of an optimal line balance could be infinitely large we also establish some lower and upper bounds for a finite stability radius third we derive formulae that are needed and develop an algorithm for obtaining the stability radius of an optimal line balance

sharp convergence rate of eigenvalues in a domain with a shrinking tube abstract in this paper we consider a class of singularly perturbed domains obtained by attaching a cylindrical tube to a fixed bounded region and letting its section shrink to zero we use an almgren type monotonicity formula to evaluate the sharp convergence rate of perturbed simple eigenvalues via courant fischer min max characterization and blow up analysis for scaled eigenfunctions

domain perturbation for linear and nonlinear parabolic equations abstract we shall develop a general theory for domain perturbation for linear and nonlinear parabolic equations with measurable coefficients subject to dirichlet boundary conditions we show how solutions of linear and nonlinear parabolic equations behave as a sequence of domains approaches an open set convergence of domains is understood in a very general sense which allows that certain parts of the domains degenerate and are deleted in the limit or that small sets are removed we also consider the periodic problem and establish existence and uniqueness results for periodic solutions for the perturbed problem in a neighborhood of a periodic solution of the original equation the theory can be used for instance to construct domains where a given nonlinear periodic parabolic equation has many periodic solutions

a chance constrained approach to stochastic line balancing problem abstract in this paper chance constrained 0 1 integer programming models for the stochastic traditional and u type line balancing ulb problem are developed these models are solved for several test problems that are well known in the literature and the computational results are given in addition a goal programming approach is presented in order to increase the system reliability which is arising from the stochastic case

generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains using three different notions of the generalized principal eigenvalue of linear second order elliptic operators in unbounded domains we derive necessary and sufficient conditions for the validity of the maximum principle as well as for the existence of positive eigenfunctions for the dirichlet problem relations between these principal eigenvalues their simplicity and several other properties are further discussed 2015 wiley periodicals inc

an linear programming based lower bound for the simple assembly line balancing problem the simple assembly line balancing problem is a classical integer programming problem in operations research a set of tasks each one being an indivisible amount of work requiring a number of time units must be assigned to workstations without exceeding the cycle time we present a new lower bound namely the lp relaxation of an integer programming formulation based on dantzig wolfe decomposition we propose a column generation algorithm to solve the formulation therefore we develop a branch and bound algorithm to exactly solve the pricing problem we assess the quality of the lower bound by comparing it with other lower bounds and the best known solution of the various instances from the literature computational results show that the lower bound is equal to the best known objective function value for the majority of the instances moreover the new lp based lower bound is able to prove optimality for an open problem c 2004 elsevier b v all rights reserved

cost oriented assembly line balancing model formulations solution difficulty upper and lower bounds abstract this paper deals with cost oriented assembly line balancing first we focus on the special objective function and a formal problem statement then we concentrate on general model formulations that can be solved by standard optimisation tools and introduce several improvements to existent models these models are designed for either general branch and bound techniques with lp relaxation or general implicit enumeration techniques further we discuss the solution difficulty of the problem and show that the maximally loaded station rule has to be replaced by the two stations rule compared to the time oriented version this causes an enormous increase in solution difficulty we introduce improved and new bounds for the number of stations and for the relevant costs per product unit these are used in the general model formulations as well as in specially designed optimisation methods finally we give a brief overview of these specially designed methods that are discussed in detail in amen 2000a b 2001

a heuristic algorithm for a chance constrained stochastic program a chance constrained stochastic program is considered that arises from an application to college enrollments and in which the objective function is the expectation of a linear function of the random variables when these random variables are independent and normally distributed with mean and variance that are linear in the decision variables the deterministic equivalent of the problem is a nonconvex nonlinear knapsack problem the optimal solution to this problem is characterized and a greedy type heuristic algorithm that exploits this structure is employed computational results show that the algorithm performs well especially when the normal random variables are approximations of binomial random variables

spectral stability of general non negative self adjoint operators with applications to neumann type operators we prove a stability theorem for the eigenvalues of general non negative self adjoint linear operators with compact resolvents and by applying it we prove a sharp stability result for the dependence of the eigenvalues of second order uniformly elliptic linear operators with homogeneous neumann boundary conditions upon domain perturbation

assembly system design a branch and cut approach this paper addresses the single product assembly system design problem asdp which seeks to minimize total cost by optimally integrating design selecting the machine type to locate at each activated station and operating issues assigning tasks to observe precedence relationships and cycle time restrictions we propose an effective branch and cut approach for solving single product asdps adapting inequalities known to be valid for embedded line balancing structures to form inequalities that are valid for the asdp the implementation alsoinvolves a specialized preprocessor a heuristic separation procedures and an enumeration scheme computational tests establish benchmark results for this first implementation of cutting planes for solving the asdp

spectral stability of the neumann laplacian we prove the equivalence of hardy and sobolev type inequalities certain uniform bounds on the heat kernel and some spectral regularity properties of the neumann laplacian associated with an arbitrary region of finite measure in euclidean space we also prove that if one perturbs the boundary of the region within a uniform holder category then the eigenvalues of the neumann laplacian change by a small and explicitly estimated amount

on differentiability of eigenvalues of second order elliptic operators on non smooth domains abstract the regularity of eigenvalues of elliptic operators upon deformations of a given bounded domain is a classical problem in elliptic pdes which has been focused by many authors we establish a theorem on c r dependence of algebraically simple eigenvalues and eigenfunctions with respect to perturbations of c 1 class of non smooth domains and of c r class of coefficients of elliptic operators moreover we also compute the first variation of these eigenvalues in relation to both parameters for non smooth domains as a byproduct we extend hadamard s formula to second order elliptic operators for domains of c 2 class and other non smooth ones

fuzzy chance constrained linear programming model for optimizing the scrap charge in steel production optimizing the charge in secondary steel production is challenging because the chemical composition of the scrap is highly uncertain the uncertainty can cause a considerable risk of the scrap mix failing to satisfy the composition requirements for the final product in this paper we represent the uncertainty based on fuzzy set theory and constrain the failure risk based on a possibility measure consequently the scrap charge optimization problem is modeled as a fuzzy chance constrained linear programming problem since the constraints of the model mainly address the specification of the product the crisp equivalent of the fuzzy constraints should be less relaxed than that purely based on the concept of soft constraints based on the application context we adopt a strengthened version of soft constraints to interpret fuzzy constraints and form a crisp model with consistent and compact constraints for solution simulation results based on realistic data show that the failure risk can be managed by proper combination of aspiration levels and confidence factors for defining fuzzy numbers there is a tradeoff between failure risk and material cost the presented approach applies also for other scrap based production processes