a warm start approach for large scale stochastic linear programs we describe a way of generating a warm start point for interior point methods in the context of stochastic programming our approach exploits the structural information of the stochastic problem so that it can be seen as a structure exploiting initial point generator we solve a small scale version of the problem corresponding to a reduced event tree and use the solution to generate an advanced starting point for the complete problem the way we produce a reduced tree tries to capture the important information in the scenario space while keeping the dimension of the corresponding reduced deterministic equivalent small we derive conditions which should be satisfied by the reduced tree to guarantee a successful warm start of the complete problem the implementation within the hopdm and oops interior point solvers shows remarkable advantages

an interior point method for bordered block diagonal linear programs this paper presents an interior point method for solving a bordered block diagonal linear program which consists of a number of disjoint blocks coupled by a total of p variables and constraints this structure includes the well known block angular and dual block angular structures as well as their special cases such as staircase problems generalized bounds and multicommodity flows when p is small relative to the total dimension of the problem the method achieves a substantial speedup relative to other general purpose methods

an interior point method for block angular optimization an interior point method for block angular optimization is developed and the convergence properties of the method are described a major motivation for such a method is that most of the computation is easily parallelized computational results are presented for a class of large scale linear programming models these models are multicommodity flow problems that arise from an air force military airlift command application and generate problems as large as 100 000 rows and 300 000 columns

a new nonstationarity detector a new test to determine the stationarity length of a locally wide sense stationary gaussian random process is proposed based on the modeling of the process as a time varying autoregressive process the time varying model parameters are tested using a rao test the use of a rao test avoids the necessity of obtaining the maximum likelihood estimator of the model parameters under the alternative hypothesis which is intractable computer simulation results are given to demonstrate its effectiveness and to verify the asymptotic theoretical performance of the test applications are to spectral analysis noise estimation and time series modeling

multicommodity network flows the impact of formulation on decomposition this paper investigates the impact of problem formulation on dantzig wolfe decomposition for the multicommodity network flow problem these problems are formulated in three ways origin destination specific destination specific and product specific the path based origin destination specific formulation is equivalent to the tree based destination specific formulation by a simple transformation supersupply and superdemand nodes are appended to the tree based product specific formulation to create an equivalent path based product specific formulation we show that solving the path based problem formulations by decomposition results in substantially fewer master problem iterations and lower cpu times than by using decomposition on the equivalent tree based formulations computational results on a series of multicommodity network flow problems are presented

mode identification of volatility in time varying autoregression in many applications time series exhibit nonstationary behavior that might reasonably be modeled as a time varying autoregressive ar process in the context of such a model we discuss the problem of testing for modality of the variance function we propose a test of modality that is local and when used iteratively can be used to identify the total number of modes in a given series this problem is closely related to peak detection and identification which has applications in many fields we propose a test that under appropriate assumptions is asymptotically distribution free under the null hypothesis even though nonparametric estimation of the ar parameter functions is involved simulation studies and applications to real datasets illustrate the behavior of the test

using an interior point method for the master problem in a decomposition approach abstract we address some of the issues that arise when an interior point method is used to handle the master problem in a decomposition approach the main points concem the efficient exploitation of the special structure of the master problem to reduce the cost of a single interior point iteration the particular structure is the presence of gub constraints and the natural partitioning of the constraint matrix into blocks built of cuts generated by different subproblems the method can be used in a fairly general case i e in any decomposition approach whenever the master is solved by an interior point method in which the normal equations are used to compute orthogonal projections computational results demonstrate its advantages for one particular decomposition approach analytic center cutting plane method accpm is applied to solve large scale nonlinear multicommodity network flow problems up to 5000 arcs and 10000 commodities

dual multilevel optimization we study the structure of dual optimization problems associated with linear constraints bounds on the variables and separable cost we show how the separability of the dual cost function is related to the sparsity structure of the linear equations as a result techniques for ordering sparse matrices based on nested dissection or graph partitioning can be used to decompose a dual optimization problem into independent subproblems that could be solved in parallel the performance of a multilevel implementation of the dual active set algorithm is compared with cplex simplex and barrier codes using netlib linear programming test problems

overgroups of a unitary group in gl 2 k abstract all the overgroups of a 2 dimensional unitary tu 2 k q l in gl 2 k are determined for an arbitrary division ring k

on geometrical properties of preconditioners in ipms for classes of block angular problems one of the most efficient interior point methods for some classes of block angular structured problems solves the normal equations by a combination of cholesky factorizations and preconditioned conjugate gradient for respectively the block and linking constraints in this work we show that the choice of a good preconditioner depends on geometrical properties of the constraint structure in particular the principal angles between the subspaces generated by the diagonal blocks and the linking constraints can be used to estimate ex ante the efficiency of the preconditioner numerical validation is provided with some generated optimization problems an application to the solution of multicommodity network flow problems with nodal capacities and equal flows of up to 64 million variables and up to 7 9 million constraints is also presented these computational results also show that predictor corrector directions combined with iterative system solves can be a competitive option for large instances

narrowband acoustic doppler volume backscattering signal ii spectral centroid estimation for pt i see ibid vol 50 p 2644 2655 2002 this paper proposes a novel algorithm to estimate the time varying spectral centroid of the narrowband doppler volume backscattering signal it is constructed in a semi parametric way that is modeling parametrically the local narrowband evolutionary spectrum using an ar 2 and nonparametrically adapting its time varying coefficients using the wavelet shrinkage the improved performance is gained by the underlying linear prediction function of the ar 2 and the minimax optimality of the unknown smoothness adaptation of the wavelet shrinkage procedure

generalized feature extraction for time varying autoregressive models in this paper a feature extraction scheme for a general type of nonstationary time series is described a non stationary time series is one in which the statistics of the process are a function of time this time dependency makes it impossible to utilize standard globally derived statistical attributes such as autocorrelations partial correlations and higher order moments as features in order to overcome this difficulty the time series vectors are considered within a finite time interval and are modeled as time varying autoregressive ar processes the ar coefficients that characterize the process are functions of time that may be represented by a family of basis vectors a novel bayesian formulation is developed that allows the model order of a time varying ar process as well as the form of the family of basis vectors used in the representation of each of the ar coefficients to be determined the corresponding basis coefficients are then invariant over the time window and since they directly relate to the time varying ar coefficients are suitable features for discrimination results illustrate the effectiveness of the method

overgroups of classical groups in linear group over banach algebras abstract all overgroups of elementary unitary groups in linear group gl 2 n over banach algebras with 1 have been described

a cutting plane approach for large scale capacitated multi period facility location using a specialized interior point method we propose a cutting plane approach namely benders decomposition for a class of capacitated multi period facility location problems the novelty of this approach lies on the use of a specialized interior point method for solving the benders subproblems the primal block angular structure of the resulting linear optimization problems is exploited by the interior point method allowing the either exact or inexact efficient solution of large instances the consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting plane method the methodology proposed allowed the solution of instances of up to 200 potential locations one million customers and three periods resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables those problems were solved by the specialized approach in less than one hour and a half outperforming other state of the art methods which exhausted the 144 gb of available memory in the largest instances

overgroups of the elementary unitary group in linear group over commutative rings abstract for a commutative ring with identity we give a complete description of all overgroups of the elementary unitary group eu 2 n r n 5 in linear group gl 2 n r

improving an interior point approach for large block angular problems by hybrid preconditioners abstract the computational time required by interior point methods is often dominated by the solution of linear systems of equations an efficient specialized interior point algorithm for primal block angular problems has been used to solve these systems by combining cholesky factorizations for the block constraints and a conjugate gradient based on a power series preconditioner for the linking constraints in some problems this power series preconditioner resulted to be inefficient on the last interior point iterations when the systems became ill conditioned in this work this approach is combined with a splitting preconditioner based on lu factorization which works well for the last interior point iterations computational results are provided for three classes of problems multicommodity flows oriented and nonoriented minimum distance controlled tabular adjustment for statistical data protection and the minimum congestion problem the results show that in most cases the hybrid preconditioner improves the performance and robustness of the interior point solver in particular for some block angular problems the solution time is reduced by a factor of 10

a specialized interior point algorithm for multicommodity network flows despite the efficiency shown by interior point methods in large scale linear programming they usually perform poorly when applied to multicommodity flow problems the new specialized interior point algorithm presented here overcomes this drawback this specialization uses both a preconditioned conjugate gradient solver and a sparse cholesky factorization to solve a linear system of equations at each iteration of the algorithm the ad hoc preconditioner developed by exploiting the structure of the problem is instrumental in ensuring the efficiency of the method an implementation of the algorithm is compared to state of the art packages for multicommodity flows the computational experiments were carried out using an extensive set of test problems with sizes of up to 700 000 variables and 150 000 constraints the results show the effectiveness of the algorithm

parallel interior point solver for structured linear programs issues of implementation of an object oriented library for parallel interior point methods are addressed the solver can easily exploit any special structure of the underlying optimization problem in particular it allows a nested embedding of structures and by this means very complicated real life optimization problems can be modelled the efficiency of the solver is illustrated on several problems arising in the optimization of networks the sequential implementation outperforms the state of the art commercial optimization software the parallel implementation achieves speed ups of about 3 1 3 9 on 4 processors parallel systems and speed ups of about 10 12 on 16 processors parallel systems

exploiting special structure in a primal dual path following algorithm a primal dual path following algorithm that applies directly to a linear program of the form min ctx ax b hx u x 0 x n is presented this algorithm explicitly handles upper bounds generalized upper bounds variable upper bounds and block diagonal structure we also show how the structure of time staged problems and network flow problems can be exploited especially on a parallel computer finally using our algorithm we obtain a complexity bound of o sqrt n ds2 log nk fortransportation problems withs origins d destinations s

quadratic regularizations in an interior point method for primal block angular problems one of the most efficient interior point methods for some classes of primal block angular problems solves the normal equations by a combination of cholesky factorizations and preconditioned conjugate gradient for respectively the block and linking constraints its efficiency depends on the spectral radius in 0 1 of a certain matrix in the definition of the preconditioner spectral radius close to 1 degrade the performance of the approach the purpose of this work is twofold first to show that a separable quadratic regularization term in the objective reduces the spectral radius significantly improving the overall performance in some classes of instances second to consider a regularization term which decreases with the barrier function thus with no need for an extra parameter computational experience with some primal block angular problems confirms the efficiency of the regularized approach in particular for some difficult problems the solution time is reduced by a factor of two to ten by the regularization term outperforming state of the art commercial solvers

computing block angular karmarkar projections with applications to stochastic programming we present a variant of karmarkar s algorithm for block angular structured linear programs such as stochastic linear programs by computing the projection efficiently we give a worst case bound on the order of the running time that can be an order of magnitude better than that of karmarkar s standard algorithm further implications for approximations and very large scale problems are given

reoptimization with the primal dual interior point method reoptimization techniques for an interior point method applied to solving a sequence of linear programming problems are discussed conditions are given for problem perturbations that can be absorbed in merely one newton step the analysis is performed for both short step and long step feasible path following methods a practical procedure is then derived for an infeasible path following method it is applied in the context of crash start for several large scale structured linear programs numerical results with oops a new object oriented parallel solver demonstrate the efficiency of the approach for large structured linear programs crash start leads to about 40 reduction in the number of iterations and translates into a 25 reduction of the solution time the crash procedure parallelizes well and speed ups between 3 1 3 8 on four processors are achieved

parallel factorization of structured matrices arising in stochastic programming solving the deterministic equivalent formulation of two stage stochastic programs using interior point algorithms requires the solution of linear systems of the form left ad 2 a top right dy b the constraint matrix a has a dual block angular structure we develop a parallel matrix factorization procedure using the sherman morrison woodbury formula based on the work of birge and qi management sci 34 1988 pp 1472 1479 this procedure requires the solution of smaller independent systems of equations with the use of optimal communication algorithms and careful attention to data layout a parallel implementation is obtained that achieves near perfect speedup scalable performance is observed on an intel ipsc 860 hypercube and a connection machine cm 5 results are reported with the solution of the linear systems arising when solving stochastic programs with up to 98 304 scenarios which correspond to deterministic equivalent linear programs with up to 1 966 090 constraints and 13 762 6

staircase matrices and systems difference equations spline approximations and multiperiod linear programs all give rise to linear equation systems that have a characteristic staircase structure a staircase system s variables can be partitioned into a natural sequence of periods in such a way that every equation involves at most the variables of two adjacent periods this paper surveys the numerous properties of staircase systems and of the staircase matrices that comprise their coefficients particular attention is given to reduced and sparse staircase forms and to the varieties of gaussian elimination for solving staircase systems

overgroups of symplectic group in linear group over commutative rings abstract for a commutative ring with identity 1 we give a complete description of all overgroups of symplectic group sp 2 n r where either n 3 or n 2 and r has no factor ring of two elements in general linear group gl 2 n r