differential approximation of min sat max sat and related problems we present differential approximation results both positive and negative for optimal satisfiability optimal constraint satisfaction and some of the most popular restrictive versions of them as an important corollary we exhibit an interesting structural difference between the landscapes of approximability classes in standard and differential paradigms

the traveling salesman problem with distances one and two we present a polynomial time approximation algorithm with worst case ratio 7 6 for the special case of the traveling salesman problem in which all distances are either one or two we also show that this special case of the traveling salesman problem is max snp hard and therefore it is unlikely that it has a polynomial time approximation scheme

an fptas for optimizing a class of low rank functions over a polytope we present a fully polynomial time approximation scheme fptas for optimizing a very general class of non linear functions of low rank over a polytope our approximation scheme relies on constructing an approximate pareto optimal front of the linear functions which constitute the given low rank function in contrast to existing results in the literature our approximation scheme does not require the assumption of quasi concavity on the objective function for the special case of quasi concave function minimization we give an alternative fptas which always returns a solution which is an extreme point of the polytope our technique can also be used to obtain an fptas for combinatorial optimization problems with non linear objective functions for example when the objective is a product of a fixed number of linear functions we also show that it is not possible to approximate the minimum of a general concave function over the unit hypercube to within any factor unless p np we prove this by showing a similar hardness of approximation result for supermodular function minimization a result that may be of independent interest

an fptas for minimizing the product of two non negative linear cost functions we consider a quadratic programming qp problem of the form min x t c x subject to ax b x 0 where c in mathbb r n times n rm rank c 1 and a in mathbb r m times n b in mathbb r m we present an fully polynomial time approximation scheme fptas for this problem by reformulating the qp as a parameterized lp and rounding the optimal solution furthermore our algorithm returns an extreme point solution of the polytope therefore our results apply directly to 0 1 problems for which the convex hull of feasible integer solutions is known such as spanning tree matchings and sub modular flows they also apply to problems for which the convex hull of the dominant of the feasible integer solutions is known such as s t shortest paths and s t min cuts for the above discrete problems the quadratic program models the problem of obtaining an integer solution that minimizes the product of two linear non negative cost functions

an improved approximation algorithm for the maximum tsp in this paper we consider the maximum traveling salesman problem with c parameterized triangle inequality for c 12 1 which means that the edge weights in the given complete graph g v e w satisfy w uv c w ux w xv for all distinct nodes u x v v for the maximum traveling salesman problem with c parameterized triangle inequality r hassin and s rubinstein gave a constant factor approximation algorithm with polynomial running time they achieved a performance ratio c only for c 12 57 in 8 which is the best known result we design a k c 1 2 ck c approximation algorithm for the maximum traveling salesman problem with c parameterized triangle inequality by using a similar idea but very different method to that in 11 where k min c i i 1 2 m c 1 c 2 c m is an optimal solution of the minimum cycle cover in g which is better than the c approximation algorithm for almost all c 12 1

approximating the pareto curve with local search for the bicriteria tsp 1 2 problem local search has been widely used in combinatorial optimization local search in combinatorial optimization wiley new york 1997 however in the case of multicriteria optimization almost no results are known concerning the ability of local search algorithms to generate good solutions with performance guarantee in this paper we introduce such an approach for the classical traveling salesman problem tsp problem proc stoc 00 2000 pp 126 133 we show that it is possible to get in linear time a 3 2 approximate pareto curve using an original local search procedure based on the 2 opt neighborhood for the bicriteria tsp 1 2 problem where every edge is associated to a couple of distances which are either 1 or 2 math oper res 18 1 1993 1

on tail dependence coefficients of transformed multivariate archimedean copulas this paper presents the impact of a class of transformations of copulas in their upper and lower multivariate tail dependence coefficients in particular we focus on multivariate archimedean copulas in the first part of this paper we calculate multivariate transformed tail dependence coefficients when the generator of the considered transformed copula exhibits some regular variation properties and we investigate the behaviour of these coefficients in cases that are close to tail independence we obtain new results under specific conditions involving regularly varying hazard rates of components of the transformation these results are also valid for non transformed archimedean copulas in the second part we deal with transformations presented by di bernardino and rulliere 20 we show the utility of using transformed archimedean copulas as they permit to build archimedean generators exhibiting any chosen couple of lower and upper tail dependence coefficients finally we detail the extreme behaviour of the transformed radial part of archimedean copulas using results in larsson and neslehova 52 and we explain possible applications with transformed markov chains

on an approximation measure founded on the links between optimization and polynomial approximation theory in order to define a polynomial approximation theory linked to combinatorial optimization closer than the existing one we first formally define the notion of a combinatorial optimization problem and then based upon this notion we introduce a notion of equivalence among optimization problems this equivalence includes for example translation or affine transformation of the objective function or yet some aspects of equivalencies between maximization and minimization problems for example the equivalence between minimum vertex cover and maximum independent set next we adress the question of the adoption of an approximation ratio respecting the defined equivalence we prove that an approximation ratio defined as a two variable function cannot respect this equivalence we then adopt a three variable function as a new approximation ratio already used by a number of researchers which is coherent to the equivalence and under the choice of the variables the new ratio is introduced by an axiomatic approach finally using the new ratio we prove approximation results for a number of combinatorial problems

effects of error covariance structure on estimation of model averaging weights and predictive performance 1 when conducting model averaging for assessing groundwater conceptual model uncertainty the averaging weights are often evaluated using model selection criteria such as aic aicc bic and kic akaike information criterion corrected akaike information criterion bayesian information criterion and kashyap information criterion respectively however this method often leads to an unrealistic situation in which the best model receives overwhelmingly large averaging weight close to 100 which cannot be justified by available data and knowledge it was found in this study that this problem was caused by using the covariance matrix c of measurement errors for estimating the negative log likelihood function common to all the model selection criteria this problem can be resolved by using the covariance matrix cek of total errors including model errors and measurement errors to account for the correlation between the total errors an iterative two stage method was developed in the context of maximum likelihood inverse modeling to iteratively infer the unknown cek from the residuals during model calibration the inferred cek was then used in the evaluation of model selection criteria and model averaging weights while this method was limited to serial data using time series techniques in this study it can be extended to spatial data using geostatistical techniques the method was first evaluated in a synthetic study and then applied to an experimental study in which alternative surface complexation models were developed to simulate column experiments of uranium reactive transport it was found that the total errors of the alternative models were temporally correlated due to the model errors the iterative two stage method using cek resolved the problem that the best model receives 100 model averaging weight and the resulting model averaging weights were supported by the calibration results and physical understanding of the alternative models using cek obtained from the iterative two stage method also improved predictive performance of the individual models and model averaging in both synthetic and experimental studies

parameter identification of groundwater aquifer models a generalized least squares approach this paper concerns the methods of estimating aquifer transmissivities on the basis of unsteady state hydraulic head data traditionally the criterion of minimizing the sum of the squares of errors has been used to match the observed data with the model response the data used for optimization usually contain noise that is not necessarily uncorrelated it is well understood that the results of identification methods are very sensitive to measurement errors in data in this study the ordinary least squares ols technique is carried out along with a generalized least squares gls technique specifically designed to reduce the effect of correlated errors the trace of the covariance matrix is used as a measure of overall accuracy and reliability of the estimated parameters the effectiveness of the ols and gls techniques in dealing with noisy data is demonstrated by using a hypothetical example the results of numerical experiments suggest that gls offers a promising approach in efficiently improving the reliability of the estimated parameters

approximation algorithms for indefinite quadratic programming we consider approximation schemes for indefinite quadratic programming we argue that such an approximation can be found in polynomial time for fixed andt wheret denotes the number of negative eigenvalues of the quadratic term our algorithm is polynomial in 1 for fixedt and exponential int for fixed we next look at the special case of knapsack problems showing that a more efficient polynomial int approximation algorithm exists

some optimal inapproximability results we prove optimal up to an arbitrary e 0 inapproximability results for max e k sat for k 3 maximizing the number of satisfied linear equations in an over determined system of linear equations modulo a prime p and set splitting as a consequence of these results we get improved lower bounds for the efficient approximability of many optimization problems studied previously in particular for max e2 sat max cut max di cut and vertex cover

a trust region strategy for minimization on arbitrary domains we present a trust region method for minimizing a general differentiable function restricted to an arbitrary closed set we prove a global convergence theorem the trust region method defines difficult subproblems that are solvable in some particular cases we analyze in detail the case where the domain is a euclidean ball for this case we present numerical experiments where we consider different hessian approximations

incorporation of prior information on parameters into nonlinear regression groundwater flow models 1 theory prior information on the parameters of a groundwater flow model can be used to improve parameter estimates obtained from nonlinear regression solution of a modeling problem two scales of prior information can be available 1 prior information having known reliability that is bias and random error structure and 2 prior information consisting of best available estimates of unknown reliability a regression method that incorporates the second scale of prior information assumes the prior information to be fixed for any particular analysis to produce improved although biased parameter estimates approximate optimization of two auxiliary parameters of the formulation is used to help minimize the bias which is almost always much smaller than that resulting from standard ridge regression it is shown that if both scales of prior information are available then a combined regression analysis may be made

estimation of copula based semiparametric time series models this paper studies the estimation of a class of copula based semiparametric stationary markov models these models are characterized by nonparametric marginal distributions and parametric copula functions while the copulas capture all the scale free temporal dependence of the processes simple estimators of the marginal distribution and the copula parameter are provided and their asymptotic properties are established under easily verifiable conditions these results are used to obtain root n consistent and asymptotically normal estimators of important features of the transition distribution such as the nonlinear conditional moments and conditional quantiles the semiparametric conditional quantile estimators are automatically monotonic across quantiles which is attractive for portfolio conditional value at risk calculations

a tutorial on the use of graph coloring for some problems in robotics we study the problem where a robot has to pick up items of different sizes which are stored along a corridor a natural requirement is that the items have to be collected in decreasing order of their sizes we deal with various systems according to the location of the entry exit station where the robot unloads the collected items after each trip along the corridor the links of these systems with generalized coloring problems and other applications such that train shunting and pallet loading problems are discussed and related results are obtained we conclude with several open questions on the topic

copula based time series with filtered nonstationarity abstract economic and financial time series data can exhibit nonstationary and nonlinear patterns simultaneously this paper studies copula based time series models that capture both patterns we introduce a procedure where nonstationarity is removed via a filtration and then the nonlinear temporal dependence in the filtered data is captured via a flexible markov copula we propose two estimators of the copula dependence parameters the parametric two step copula estimator where the marginal distribution of the filtered series is estimated parametrically and the semiparametric two step copula estimator where the marginal distribution is estimated via a rescaled empirical distribution of the filtered series we show that the limiting distribution of the parametric copula estimator depends on the nonstationary filtration and the parametric marginal distribution estimation and may be non normal surprisingly the limiting distribution of the semiparametric copula estimator using the filtered data is shown to be the same as that without nonstationary filtration which is normal and free of marginal distribution specification the simple and robust properties of the semiparametric copula estimators extend to models with misspecified copulas and facilitate statistical inferences such as hypothesis testing and model selection tests on semiparametric copula based dynamic models in the presence of nonstationarity monte carlo studies and real data applications are presented

on the differential approximation of min set cover we present in this paper differential approximation results for min set cover and min weighted set cover we first show that the differential approximation ratio of the natural greedy algorithm for min set cover is bounded below by 1 365 and above by 4 1 where is the maximum set cardinality in the min set cover instance next we study another approximation algorithm for min set cover that computes 2 optimal solutions i e solutions that cannot be improved by removing two sets belonging to them and adding another set not belonging to them we prove that the differential approximation ratio of this second algorithm is bounded below by 2 1 and that this bound is tight finally we study an approximation algorithm for min weighted set cover and provide a tight lower bound of 1 our results identically hold for max hypergraph independent set in both the standard and the differential approximation paradigms

approximation algorithms for the maximum hamiltonian path problem with specified endpoint s abstract this paper deals with the problem of constructing hamiltonian paths of optimal weight called hpps t if the two endpoints are specified hpps if only one endpoint is specified we show that hpps t is 1 2 differential approximable and hpps is 2 3 differential approximable moreover we observe that these problems cannot be differential approximable better than 741 742 based upon these results we obtain new bounds for standard ratio a 1 2 standard approximation for m ax hpps t and a 2 3 for m ax hpps which can be improved to 2 3 for m ax hpps t a 2a all the edge weights are within an interval a 2a to 5 6 for m ax hpps a 2a and to 2 3 for m in hpps t a 2a to 3 4 for m in hpps a 2a

the inverse problem for confined aquifer flow identification and estimation with extensions the contributions of this work are twofold first a methodology for estimating the elements of parameter matrices in the governing equation of flow in a confined aquifer is developed the estimation techniques for the distributed parameter inverse problem pertain to linear least squares and generalized least squares methods the linear relationship among the known heads and unknown parameters of the flow equation provides the background for developing criteria for determining the identifiability status of unknown parameters under conditions of exact or overidentification it is possible to develop statistically consistent parameter estimators and their asymptotic distributions the estimation techniques namely two stage least squares and three stage least squares are applied to a specific groundwater inverse problem and compared between themselves and with an ordinary least squares estimator the three stage estimator provides the closer approximation to the actual parameter values but it also shows relatively large standard errors as compared to the ordinary and two stage estimators the estimation techniques provide the parameter matrices required to simulate the unsteady groundwater flow equation second a nonlinear maximum likelihood estimation approach to the inverse problem is presented the statistical properties of maximum likelihood estimators are derived and a procedure to construct confidence intervals and do hypothesis testing is given the relative merits of the linear and maximum likelihood estimators are analyzed other topics relevant to the identification and estimation methodologies i e a continuous time solution to the flow equation coping with noise corrupted head measurements and extension of the developed theory to nonlinear cases are also discussed a simulation study is used to evaluate the methods developed in this study

bose einstein condensation in satisfiability problems abstract this paper is concerned with the complex behavior arising in satisfiability problems we present a new statistical physics based characterization of the satisfiability problem specifically we design an algorithm that is able to produce graphs starting from a k sat instance in order to analyze them and show whether a bose einstein condensation occurs we observe that analogously to complex networks the networks of k sat instances follow bose statistics and can undergo bose einstein condensation in particular k sat instances move from a fit get rich network to a winner takes all network as the ratio of clauses to variables decreases and the phase transition of k sat approximates the critical temperature for the bose einstein condensation finally we employ the fitness based classification to enhance sat solvers e g chainsat and obtain the consistently highest performing sat solver for cnf formulas and therefore a new class of efficient hardware and software verification tools

reductions completeness and the hardness of approximability in computability and in complexity theory reductions are widely used for mapping sets into sets in order to prove undecidability or hardness results in the study of the approximate solvability of hard discrete optimization problems suitable kinds of reductions called approximation preserving reductions can also be used to transfer from one problem to another either positive results solution techniques or negative results non approximability results in this paper various kinds of approximation preserving reductions are surveyed and their properties discussed the role of completeness under approximation preserving reductions is also analyzed and its relationship with hardness of approximability is explained

structure in approximation classes the study of the approximability properties of np hard optimization problems has recently made great advances mainly due to the results obtained in the field of proof checking the last important breakthrough proves the apx completeness of several important optimization problems and thus reconciles two distinct views of approximation classes syntactic and computational s khanna et al in proc 35th ieee symp on foundations of computer science ieee computer society press los alamitos ca 1994 pp 819 830 in this paper we obtain new results on the structure of several computationally defined approximation classes in particular after defining a new approximation preserving reducibility to be used for as many approximation classes as possible we give the first examples of natural npo complete problems and the first examples of natural apx intermediate problems moreover we state new connections between the approximability properties and the query complexity of npo problems

estimation of aquifer parameters under transient and steady state conditions 1 maximum likelihood method incorporating prior information in this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions the parameters include values and directions of principal hydraulic conductivities or transmissivities in anisotropic media specific storage or storativity interior and boundary recharge or leakage rates coefficients of head dependent interior and boundary sources and boundary heads in transient situations the initial head distribution can also be estimated if the system is originally at a steady state paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters the inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters since not all the factors which contribute to the prior errors can be quantified statistically at the outset the covariance matrices of these errors are expressed in terms of several parameters which if unknown can be estimated jointly with the hydraulic parameters by a stagewise optimization process when transient head data are separated by a fixed time interval the temporal structure of these data is approximated by a lag one autoregressive model with a correlation coefficient that can be treated as another unknown parameter estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature all of which are based on the maximum likelihood concept might be useful for selecting the best groundwater model or the best method of parameterizing a particular model among a number of given alternatives

an extension of karmarkar projective algorithm for convex quadratic programming we present an extension of karmarkar s linear programming algorithm for solving a more general group of optimization problems convex quadratic programs this extension is based on the iterated application of the objective augmentation and the projective transformation followed by optimization over an inscribing ellipsoid centered at the current solution it creates a sequence of interior feasible points that converge to the optimal feasible solution in o ln iterations each iteration can be computed in o ln3 arithmetic operations wheren is the number of variables andl is the number of bits in the input in this paper we emphasize its convergence property practical efficiency and relation to the ellipsoid method

new approximation algorithms for graph coloring the problem of coloring a graph with the minimum number of colorsis well known to be np hard even restricted to k colorable graphs for constant k 3 this paper explores theapproximation problem of coloring k colorable graphs with as fewadditional colors as possible in polynomial time with special focus onthe case of k 3 the previous best upper bound on the number of colors needed forcoloring 3 colorable n vertex graphsin polynomial time was o n log n colors by berger and rompel improving a bound of o n colors by wigderson this paper presents an algorithmto color any 3 colorable graph with o n3 8 polylog n colors thus breaking an o n 1 2 o 1 barrier the algorithm given here is based on examiningsecond order neighborhoods of vertices rather than just immediateneighborhoods of vertices as in previous approaches we extend ourresults to improve the worst case bounds for coloring k colorable graphs for constant k 3 as well

efficient estimation of copula based semiparametric markov models this paper considers the efficient estimation of copula based semiparametric strictly stationary markov models these models are characterized by nonparametric invariant one dimensional marginal distributions and parametric bivariate copula functions where the copulas capture temporal dependence and tail dependence of the processes the markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications we first show that markov processes generated via clayton gumbel and student s t copulas and their survival copulas are all geometrically ergodic we then propose a sieve maximum likelihood estimation mle for the copula parameter the invariant distribution and the conditional quantiles we show that the sieve mles of any smooth functional is root n consistent asymptotically normal and efficient and that their sieve likelihood ratio statistics are asymptotically chi square distributed monte carlo studies indicate that even for markov models generated via tail dependent copulas and fat tailed marginals our sieve mles perform very well

a composite l1 parameter estimator for model fitting in groundwater flow and solute transport simulation this paper proposes a composite l1 parameter estimator to solve the inverse problems in groundwater flow and solute transport modeling the estimator is formulated using a weighted l1 norm as the error measure between the vector of the observed hydraulic heads and solute concentrations and the corresponding vector of the heads and concentrations computed from a finite element model for steady state groundwater flow and solute transport in a two dimensional areal confined aquifer system the parameters currently considered are the hydraulic conductivities the dispersivities the porosities of the aquifer system and the solute source concentration s the gradients of the state variables with respect to the parameters are computed analytically using a formulation stemming from the finite element model for the state variables the solutions to two hypothetical groundwater parameter estimation problems are presented to illustrate that the proposed estimator does have the property of being fairly accurate and more significantly being robust in handling observation data containing certain outliers

an efficient global algorithm for a class of indefinite separable quadratic programs we present a global algorithm for indefinite knapsack separable quadratic programs with bound constraints the upper bounds on variables with nonconvex terms are assumed to be infinite in the algorithmic development by characterizing optimal solutions of the problem we enumerate a subset of kkt points to determine a global optimum the enumeration is made efficient by developing a theory for shrinking and partitioning the search domain of kkt multipliers the global algorithmic procedure is developed based on interval and point testing techniques that have roots in solving strictly convex problems our algorithm has quadratic worst case complexity and its performance is demonstrated on a broad range of randomly generated problem instances and comparisons with existing global and local solvers it turns out that our method can solve these nonconvex problems of extremely large size in a fraction of the time relative to commercial software such as cplex 12 6 on a desktop computer furthermore a feasible upper bounding scheme is developed for the case when the variables with nonconvex terms are allowed to have finite upper limits using an iterative application of the above global algorithm and the computational experience is presented

aquifer parameter identification with kriging and optimum parameterization a new parameter identification method is developed for a two dimensional unsteady state groundwater flow model the method is a direct approach as it requires no iterative searching of parameters the unknown functional coefficients parameters are optimally determined by a generalized matrix inversion scheme kriging an unbiased minimum variance estimator is used as a presampling filter to reconstruct the head distribution for the entire flow domain the ill posedness of the inverse problem as characterized by instability and nonuniqueness is controlled by reparameterization utilizing the technique of finite elements a set of statistics are developed to quantify explicitly the tradeoff between the system modeling error and the error associated with the parameter uncertainty these two types of errors are shown to be a function of the parameter dimension residual mean square and trace of the covariance matrix of the estimated parameters serve as good indicators for the determination of the optimum parameter dimension a set of numerical experiments are conducted to illustrate the methodology

on the solution of concave knapsack problems we consider a version of the knapsack problem which gives rise to a separable concave minimization problem subject to bounds on the variables and one equality constraint we characterize strict local miniimizers of concave minimization problems subject to linear constraints and use this characterization to show that although the problem of determining a global minimizer of the concave knapsack problem is np hard it is possible to determine a local minimizer of this problem with at most o n logn operations and 1 logn evaluations of the function if the function is quadratic this algorithm requires at most o n logn operations

differential approximation results for the traveling salesman problem with distances 1 and 2 abstract we prove that both minimum and maximum traveling salesman problems on complete graphs with edge distances 1 and 2 denoted by min tsp12 and max tsp12 respectively are approximable within 3 4 based upon this result we improve the standard approximation ratio known for maximum traveling salesman with distances 1 and 2 from 3 4 to 7 8 finally we prove that for any 0 it is np hard to approximate both problems better than within 741 742 the same results hold when dealing with a generalization of min and max tsp12 where instead of 1 and 2 edges are valued by a and b

quadratic programming and combinatorial minimum weight product problems we present a fully polynomial time approximation scheme fptas for minimizing an objective a t x b t x under linear constraints a x d examples of such problems are combinatorial minimum weight product problems such as the following given a graph g v e and two edge weights a b e rightarrow mathbb r find an s t path p that minimizes a p b p the product of its edge weights relative to a and b

on approximation algorithms for concave mixed integer quadratic programming concave mixed integer quadratic programming is the problem of minimizing a concave quadratic polynomial over the mixed integer points in a polyhedral region in this work we describe an algorithm that finds an epsilon approximate solution to a concave mixed integer quadratic programming problem the running time of the proposed algorithm is polynomial in the size of the problem and in 1 epsilon provided that the number of integer variables and the number of negative eigenvalues of the objective function are fixed the running time of the proposed algorithm is expected unless mathcal p mathcal np

aquifer parameter identification with optimum dimension in parameterization this paper presents a systematic procedure whereby the functional coefficients imbedded in a two dimensional partial differential equation which governs unsteady groundwater flow are optimally identified the coefficients to be identified are transmissivities which vary spatially finite elements are used to represent the unknown transmissivity function parametrically in terms of nodal values over a suitable discretization of a flow region a modified gauss newton algorithm is used for parameter optimization covariance analysis is used to estimate the reliability of the estimated parameters as the dimension of the unknown parameter increases the modeling error represented by a least squares criterion will generally decrease but errors in data would be propagated to a greater degree into the estimated parameters thus reducing the reliability of estimation the reliability of the estimated parameters is characterized by a norm of the covariance matrix this information is used for the determination of the optimum dimension in parameterization

average value of solutions for the bipartite boolean quadratic programs and rounding algorithms we consider domination analysis of approximation algorithms for the bipartite boolean quadratic programming problem bbqp with m n variables a closed form formula is developed to compute the average objective function value a of all solutions in o m n time however computing the median objective function value of the solutions is shown to be np hard also we show that any solution with objective function value no worse than a dominates at least 2 m n 2 solutions and this bound is the best possible further we show that such a solution can be identified in o m n time and hence the domination ratio of this algorithm is at least 1 4 we then show that for any fixed natural numbers a and b such that a b 1 no polynomial time approximation algorithm exists for bbqp with domination ratio larger than 1 2 1 m n unless p np it is shown that some powerful local search algorithms can get trapped at a local maximum with objective function value less than a one of our approximation algorithms has an interesting rounding property which provides a data dependent lower bound on the optimal objective function value a new integer programming formulation of bbqp is also given and computational results with our rounding algorithms are reported

some np complete problems in quadratic and nonlinear programming in continuous variable smooth nonconvex nonlinear programming we analyze the complexity of checking whether a a given feasible solution is not a local minimum and b the objective function is not bounded below on the set of feasible solutions we construct a special class of indefinite quadratic programs with simple constraints and integer data and show that checking a or b on this class is np complete as a corollary we show that checking whether a given integer square matrix is not copositive is np complete

optimum experimental design for parameter identification in groundwater hydrology the experimental design for parameter identification of a confined groundwater system is formulated as a nonlinear mixed integer programming problem the decision variables considered are the number and locations of the pumping and observation wells and the pumping rates the constraints include the allowable drawdown the restricted locations of pumping wells and observation wells the permissible pumping rates and the required information the amount of the required information is determined by the prescribed reliability of the response for the future operation of the groundwater system the galerkin finite element crank nicolson approach is used to develop the simulation models for solving the groundwater governing equation for the system responses the sensitivity coefficients are computed by the influence coefficient method the principle of superposition is used to combine the simulation models with the optimization model the characteristics of the optimization problem have been investigated and are clarified and its difficulties are pointed out an efficient heuristic solution approach is proposed for solving this problem a test problem is constructed to demonstrate the usefulness of the proposed methodology observations generated from the optimal design are used to identify the parameters a covariance analysis is then carried out to verify the validity of the assumptions made in the formulation of the optimization problem the results obtained indicate that the proposed methodology is feasible and can be used to solve complicated experimental design problems associated with a confined groundwater system

review of parameter identification procedures in groundwater hydrology the inverse problem the purpose of this survey is to review parameter identification procedures in groundwater hydrology and to examine computational techniques which have been developed to solve the inverse problem parameter identification methods are classified under the error criterion used in the formulation of the inverse problem the problem of ill posedness in connection with the inverse problem is addressed typical inverse solution techniques are highlighted the review also includes the evaluation of methods used for computing the sensitivity matrix statistics which can be used to estimate the parameter uncertainty are outlined attempts have been made to compare and contrast representative inverse procedures and direction for future research is suggested

a better differential approximation ratio for symmetric tsp in this paper we study the approximability properties of symmetric tsp under an approximation measure called the differential ratio more precisely we improve up to 3 email protected for any e 0 the best differential ratio of 2 3 known so far given in hassin and khuller r hassin s khuller z approximations j algorithms 41 2 2001 429 442

differential approximation algorithms for some combinatorial optimization problems we use a new approximation measure the differential approximation ratio to derive polynomial time approximation algorithms for minimum set covering for both weighted and unweighted cases minimum graph coloring and bin packing we also propose differential approximation ratio preserving reductions linking minimum coloring minimum vertex covering by cliques minimum edge covering by cliques and minimum edge covering of a bipartite graph by complete bipartite graphs

sieve inference on possibly misspecified semi nonparametric time series models this paper establishes the asymptotic normality of plug in sieve m estimators of possibly irregular functionals of semi nonparametric time series models we show that even when the sieve score process is not a martingale difference sequence the asymptotic variance in the case of irregular functionals is the same as those for independent data using an orthonormal series long run variance estimator we construct a pre asymptotic wald statistic and show that it is asymptotically f distributed simulations indicate that our pre asymptotic wald test with f critical values has more accurate size in finite samples than the conventional wald test with chi square critical values

inverse modeling for locating dense nonaqueous pools in groundwater under steady flow conditions in this work we develop an inverse modeling procedure to identify the location and the dimensions of a single component dense nonaqueous phase liquid dnapl pool in a saturated porous medium under steady flow conditions the inverse problem is formulated as a least squares minimization problem and solved by a search procedure based on the levenberg marquardt method model output is calculated by an existing three dimensional analytical model describing the transport of solute from a dissolving distributed noise upon the forward model generated concentration field we further test the algorithm s ability to predict the location and size of a dnapl pool placed in a controlled three dimensional bench scale experiment in this case we apply the levenberg marquardt algorithm to the minimization of three types of residuals ordinary residuals weighted residuals with weights equal to the square of the inverse of the observations and weighted residuals with weights obtained by adding a constant term to the observed concentrations the results are sensitive to the location of the observation wells and to the type of residuals minimized in general better results in terms of pool location and dimensions were obtained by the minimization of weighted residuals with weights obtained by adding a constant term to the observed concentrations the results also indicate that the inverse problem is nonunique and nonconvex even in the absence of observation errors finally the sensitivity of the inverse modeling scheme to transport parameter uncertainty was addressed the inverse solution was found to be extremely sensitive to errors in the dispersion coefficients and relatively insensitive to errors in the mass transfer coefficient

on methods of sieves and penalization we develop a general theory which provides a unified treatment for the asymptotic normality and efficiency of the maximum likelihood estimates mle s in parametric semiparametric and nonparametric models we find that the asymptotic behavior of substitution estimates for estimating smooth functionals are essentially governed by two indices the degree of smoothness of the functional and the local size of the underlying parameter space we show that when the local size of the parameter space is not very large the substitution standard nonsieve substitution sieve and substitution penalized mle s are asymptotically efficient in the fisher sense under certain stochastic equicontinuity conditions of the loglikelihood moreover when the convergence rate of the estimate is slow the degree of smoothness of the functional needs to compensate for the slowness of the rate in order to achieve efficiency when the size of the parameter space is very large the standard and penalized maximum likelihood procedures may be inefficient whereas the method of sieves may be able to overcome this difficulty this phenomenon is particularly manifested when the functional of interest is very smooth especially in the semiparametric case

self normalized cramer type moderate deviations under dependence we establish a cramer type moderate deviation result for self normalized sums of weakly dependent random variables where the moment requirement is much weaker than the non self normalized counterpart the range of the moderate deviation is shown to depend on the moment condition and the degree of dependence of the underlying processes we consider three types of self normalization the equal block scheme the big block small block scheme and the interlacing scheme simulation study shows that the latter can have a better finite sample performance our result is applied to multiple testing and construction of simultaneous confidence intervals for ultra high dimensional time series mean vectors

on mutual concavity and strategically zero sum bimatrix games we study the fundamental problem 2nash of computing a nash equilibrium ne point in bimatrix games we start by proposing a novel characterization of the ne set via a bijective map to the solution set of a parameterized quadratic program neqp whose feasible space is the highly structured set of correlated equilibria ce this is to our knowledge the first characterization of the subset of ce points that are in 1 1 correspondence with the ne set of the game and contributes to the quite lively discussion on the relation between the spaces of ce and ne points in a bimatrix game e g 15 26 33 we proceed with studying a property of bimatrix games which we call mutually concavity mc that assures polynomial time tractability of 2nash due to the convexity of a proper parameterized quadratic program either neqp or a parameterized variant of the mangasarian stone formulation 23 for a particular value of the parameter we prove various characterizations of the mc games which eventually lead us to the conclusion that this class is equivalent to the class of strategically zero sum szs games of moulin vial 25 this gives an alternative explanation of the polynomial time tractability of 2nash for these games not depending on the solvability of zero sum games moreover the recognition of the mc property for an arbitrary game is much faster than the recognition szs property this along with the comparable time complexity of linear programs and convex quadratic programs leads us to a much faster algorithm for 2nash in mc games we conclude our discussion with a comparison of mc games or szs games to k rank games which are known to admit for 2nash a fptas when k is fixed 18 and a polynomial time algorithm for k 1 2 we finally explore some closeness properties under well known ne set preserving transformations of bimatrix games

local minima for indefinite quadratic knapsack problems we consider the complexity of finding a local minimum for the nonconvex quadratic knapsack problem global minimization for this example of quadratic programming is np hard more and vavasis have investigated the complexity of local minimization for the strictly concave case of qkp here we extend their algorithm to the general indefinite case our main result is an algorithm that computes a local minimum in o n logn 2 steps our approach involves eliminating all but one of the convex variables through parametrization yielding a nondifferentiable problem we use a technique from computational geometry to address the nondifferentiable problem

differential approximation for optimal satisfiability and related problems abstract we study the differential approximability of several optimization satisfiability problems we prove that unless co rp np min sat is not differential 1 m 1 e approximable for any e 0 where m is the number of clauses we also prove that any differential approximation algorithm for max minimal vertex cover can be transformed into a differential approximation algorithm for min k sat achieving the same differential performance ratio this leads us to study the differential approximability of max minimal vertex cover and min independent dominating set both of them are equivalent for the differential approximation for these problems we prove a strong inapproximability result informally unless p np any approximation algorithm has worst case approximation ratio equal to 0

efficient approximation of min set cover by moderately exponential algorithms we study the approximation of min set cover combining ideas and results from polynomial approximation and from exact computation with non trivial worst case complexity upper bounds for np hard problems we design approximation algorithms for min set cover achieving ratios that cannot be achieved in polynomial time unless problems in np could be solved by slightly super polynomial algorithms with worst case complexity much lower though super polynomial than those of an exact computation

measuring the quality of approximate solutions to zero one programming problems we point out the difficulties associated with measuring the quality of an approximate heuristic solution by percentage error as is customary we define a set of properties that are to be expected from a proper measure of solution quality and investigate the family of functions which satisfy those conditions in particular we show that for any class of 0 1 programming problems appropriate functions do exist and that they are uniquely defined up to monotone transformations we conclude with several examples of linear functions which are suitable for certain classes of problems

the complexity of approximating a nonlinear program we consider the problem of finding the maximum of a multivariate polynomial inside a convex polytope we show that there is no polynomial time approximation algorithm for this problem even one with a very poor guarantee unless p np we show that even when the polynomial is quadratic i e quadratic programming there is no polynomial time approximation unless np is contained in quasi polynomial time