a genuinely multidimensional convective pressure flux split riemann solver for euler equations a simple inexpensive genuinely multidimensional hll type riemann solver for euler equations of gasdynamics is proposed the genuinely multidimensional formulation is based on the work of balsara 17 in the present approach the missing contact wave in the hll type solver is restored using the hll cps formulation of mandal and panwar 5 a few two dimensional standard test cases are solved to demonstrate the efficacy of the proposed solver a very simple new genuinely multidimensional hll type riemann solver for euler equations is proposed due to the use of closed form expressions for the fluxes the present method is easier to apply the contact discontinuity is restored using the hll cps formulation without the need for independently specifying its direction of evolution numerical test results demonstrate the efficacy of the present method of its ability to capture accurate solutions

a genuinely multidimensional high resolution scheme for the elastic plastic wave equation in this paper we present a numerical method of high order for solving the multidimensional elastic plastic wave equation the basic idea is to decompose the hyperbolic pde into advection equations which can be solved numerically furthermore the occurrence of plasticity makes it necessary to solve an ode for the stress strain relationship at evey point

adaptive kernel search a heuristic for solving mixed integer linear programs abstract we introduce adaptive kernel search aks a heuristic framework for the solution of general mixed integer linear programs mips aks extends and enhances kernel search a heuristic framework that has been shown to produce high quality solutions for a number of specific combinatorial optimization problems in a short amount of time aks solves a sequence of carefully constructed restricted mips using a commercial mip solver the computational effort required to solve the first restricted mip guides the construction of the subsequent mips the restricted mips are constructed around a kernel which contains the variables that are presumably non zero in an optimal solution computational results for a set of 137 instances show that aks significantly outperforms other state of the art heuristics for solving mips aks also compares favorably to cplex and offers more flexibility to trade off solution quality and computing time

multidimensional upwinding part i the method of transport for solving the euler equations the aim of this paper is to show a new approach towards the discretization of multidimensional conservation laws the idea of transport associated with the solution of a scalar equation is used for the convective part of the compressible euler equations a multidimensional wave structure is derived to model the acoustic part of this non linear system that allows infinitely many propagation directions in the numerical method this provides the basic knowledge to construct a numerical method that does not rely on riemann solvers a more general definition of the waves together with the concept of consistency enables the design of a number of effective genuinely multidimensional methods

a new class of functions for measuring solution integrality in the feasibility pump approach mixed integer optimization is a powerful tool for modeling many optimization problems arising from real world applications finding a first feasible solution represents the first step for several mixed integer programming mip solvers the feasibility pump is a heuristic for finding feasible solutions to mixed integer linear programming milp problems which is effective even when dealing with hard mip instances in this work we start by interpreting the feasibility pump as a frank wolfe method applied to a nonsmooth concave merit function then we define a general class of functions that can be included in the feasibility pump scheme for measuring solution integrality and we identify some merit functions belonging to this class we further extend our approach by dynamically combining two different merit functions finally we define a new version of the feasibility pump algorithm which includes the original version of the feasibility pump as a special case and we present computational results on bi

nonlinear stability analysis for the method of transport for the elastic plastic wave equation in this paper we present an analytic assessment of the stability and convergence of the so called method of transport for solving the elastic plastic wave equation which is a nonlinear hyperbolic partial differential equation for the purely elastic wave equation which is a linear hyperbolic conservation law one can use von neumann analysis for proving that stability and convergence immediately follow from the lax equivalence theorem for plastic deformation however nonlinear stability proofs require greater effort

multidimensional upwinding part ii decomposition of the euler equations into advection equations based on a genuine multidimensional numerical scheme called the method of transport we derive a form of the compressible euler equations capable of a linearization for any space dimension this form enables a rigorous error analysis of the linearization error without the knowledge of the numerical method used to solve the linear equations the generated error can be eliminated by special correction terms in the linear equations hence existing scalar high order methods can be used to solve the linear equations and obtain high order accuracy in space and time for the non linear conservation law in this approach the scalar version of the method of transport is used to solve the linear equations this method is multidimensional and reduces the solution of the partial differential equation to an integration process convergence histories presented at the end of the paper show that the numerical results agree with the theoretical predictions

multidimensional upwind methods for hyperbolic conservation laws abstract we present a class of second order conservative finite difference algorithms for solving numerically time dependent problems for hyperbolic conservation laws in several space variables these methods are upwind and multidimensional in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge and that all fluxes are evaluated and differenced at the same time in particular operator splitting is not used correct behavior at discontinuities is obtained by the use of solutions to the riemann problem and by limiting some of the second order terms numerical results are presented which show that the methods described here yield the same high resolution as the corresponding operator split methods

octane a new heuristic for pure 0 1 programs we propose a new heuristic for pure 0 1 programs which finds feasible integer points by enumerating extended facets of the octahedron the outer polar of the unit hypercube we give efficient algorithms to carry out the enumeration and we explain how our heuristic can be embedded in a branch and cut framework finally we present computational results on a set of pure 0 1 programs taken from miplib and other sources

coordinate free ridge regression bounds abstract the dependence of ridge regression estimates on the choice of parameterization is defined with reference to the hull of all possible ridge estimates for all possible parameterizations a reanalysis of hoerl and kennard s 1970 10 factor example and marquardt and snee s 1975 acetylene data reveals that most conclusions depend on the parameterization

solving zero one mixed integer programming problems using tabu search we describe a tabu search ts approach for solving general zero one mixed integer programming mip problems that exploits the extreme point property of zero one solutions specialized choice rules and aspiration criteria are identified for the problems expressed as functions of integer infeasibility measures and objective function values the first level ts mechanisms are then extended with advanced level strategies and learning we also look at probabilistic measures in this framework and examine how the learning tool target analysis ta can be applied to identify better control structures and decision rules computational results are reported on a portfolio of multiconstraint knapsack problems our approach is designed to solve thoroughly general 0 1 mip problems and thus contains no problem domain specific knowledge yet it obtains solutions for the multiconstraint knapsack problem whose quality rivals and in some cases surpasses the best solutions obtained by special purpose methods that have been created to exploit the special structure of these problems

s values conventional context minimal measures of the sturdiness of regression coefficients this paper proposes a context minimal range of alternative regression models that is used to generate a range of alternative estimates a prior distribution is assumed with a zero mean but an ambiguous covariance matrix the choice of the prior covariance matrix is facilitated by transformation to standardized variables which makes the prior expected r2 equal to the sum of the prior variances three different ranges of the prior expected r2 are used to define three different intervals of prior covariance matrices which are used to produce three different sets of s values

robust bayesian experimental designs in normal linear models we address the problem of finding a design that minimizes the bayes risk with respect to a fixed prior subject to being robust with respect to misspecification of the prior uncertainty in the prior is formulated in terms of having a family of priors instead of one single prior two different classes of priors are considered f1 is a family of conjugate priors and a second family of priors f2 is induced by a metric on the space of nonnegative measures the family f1 has earlier been suggested by leamer and polasek while f2 was considered by derobertis and hartigan and berger the setup assumed is that of a canonical normal linear model with independent homoscedastic errors optimal robust designs are considered for the problem of estimating the vector of regression coefficients or a linear combination of the regression coefficients and also for testing and set estimation problems concrete examples are given for polynomial regression and completely randomized designs a very surprising finding is that for r2 the same design is optimal for a variety of different problems with different loss structures in general the results for f2 are significantly more substantive our results are applicable to group decision making and reconciliation of opinions among experts with different priors

a heuristic for bilp problems the single source capacitated facility location problem abstract in the single source capacitated facility location problem sscflp each customer has to be assigned to one facility that supplies its whole demand the total demand of customers assigned to each facility cannot exceed its capacity an opening cost is associated with each facility and is paid if at least one customer is assigned to it the objective is to minimize the total cost of opening the facilities and supply all the customers in this paper we extend the kernel search heuristic framework to general binary integer linear programming bilp problems and apply it to the sscflp the heuristic is based on the solution to optimality of a sequence of subproblems where each subproblem is restricted to a subset of the decision variables the subsets of decision variables are constructed starting from the optimal values of the linear relaxation variants based on variable fixing are proposed to improve the efficiency of the kernel search framework the algorithms are tested on benchmark instances and new very large scale test problems computational results demonstrate the effectiveness of the approach the kernel search algorithm outperforms the best heuristics for the sscflp available in the literature it found the optimal solution for 165 out of the 170 instances with a proven optimum the error achieved in the remaining instances is negligible moreover it achieved on 100 new very large scale instances an average gap equal to 0 64 computed with respect to a lower bound or the optimum when available the variants based on variable fixing improved the efficiency of the algorithm with minor deteriorations of the solution quality

a semi lagrangian discontinuous galerkin method for scalar advection by incompressible flows a new conservative semi lagrangian formulation is proposed for the discretization of the scalar advection equation in flux form the approach combines the accuracy and conservation properties of the discontinuous galerkin dg method with the computational efficiency and robustness of semi lagrangian sl techniques unconditional stability in the von neumann sense is proved for the proposed discretization in the one dimensional case a monotonization technique is then introduced based on the flux corrected transport approach this yields a multi dimensional monotonic scheme for the piecewise constant component of the computed solution that is characterized by a smaller amount of numerical diffusion than standard dg methods the accuracy and stability of the method are further demonstrated by two dimensional tracer advection tests in the case of incompressible flows the comparison with results obtained by standard sl and dg methods highlights several advantages of the new technique

exploring relaxation induced neighborhoods to improve mip solutions given a feasible solution to a mixed integer programming mip model a natural question is whether that solution can be improved using local search techniques local search has been applied very successfully in a variety of other combinatorial optimization domains unfortunately local search relies extensively on the notion of a solution neighborhood and this neighborhood is almost always tailored to the structure of the particular problem being solved a mip model typically conveys little information about the underlying problem structure this paper considers two new approaches to exploring interesting domain independent neighborhoods in mip the more effective of the two which we call relaxation induced neighborhood search rins constructs a promising neighborhood using information contained in the continuous relaxation of the mip model neighborhood exploration is then formulated as a mip model itself and solved recursively the second which we call guided dives is a simple modification of the mip tree traversal order loosely speaking it guides the search towards nodes that are close neighbors of the best known feasible solution extensive computational experiments on very difficult mip models show that both approaches outperform default cplex mip and a previously described approach for exploring mip neighborhoods local branching with respect to several different metrics the metrics we consider are quality of the best integer solution produced within a time limit ability to improve a given integer solution of both good and poor quality and time required to diversify the search in order to find a new solution

the feasibility pump in this paper we consider the np hard problem of finding a feasible solution if any exists for a generic mip problem of the form min ctx ax b xj integer j trivially a feasible solution can be defined as a point x p x ax b that is equal to its rounding where the rounded point is defined by x j if j and x j otherwise and represents scalar rounding to the nearest integer replacing equal with as close as possible relative to a suitable distance function x suggests the following feasibility pump fp heuristic for finding a feasible solution of a given mip we start from any x p and define its rounding at each fp iteration we look for a point x p that is as close as possible to the current by solving the problem min x x p assuming x is chosen appropriately this is an easily solvable lp problem if x 0 then x is a feasible mip solution and we are done otherwise we replace by the rounding of x and repeat we report computational results on a set of 83 difficult 0 1 mips using the commercial software ilog cplex 8 1 as a benchmark the outcome is that fp in spite of its simple foundation proves competitive with ilog cplex both in terms of speed and quality of the first solution delivered interestingly ilog cplex could not find any feasible solution at the root node for 19 problems in our test bed whereas fp was unsuccessful in just 3 cases

directional diffusion regulator ddr for some numerical solvers of hyperbolic conservation laws a computational tool called directional diffusion regulator ddr is proposed to bring forth real multidimensional physics into the upwind discretization in some numerical schemes of hyperbolic conservation laws the direction based regulator when used with dimension splitting solvers is set to moderate the excess multidimensional diffusion and hence cause genuine multidimensional upwinding like effect the basic idea of this regulator driven method is to retain a full upwind scheme across local discontinuities with the upwind bias decreasing smoothly to a minimum in the farthest direction the discontinuous solutions are quantified as gradients and the regulator parameter across a typical finite volume interface or a finite difference interpolation point is formulated based on fractional local maximum gradient in any of the weak solution flow variables say density pressure temperature mach number or even wave velocity etc ddr is applied to both the non convective as well as whole unsplit dissipative flux terms of some numerical schemes mainly of local lax friedrichs to solve some benchmark problems describing inviscid compressible flow shallow water dynamics and magneto hydrodynamics the first order solutions consistently improved depending on the extent of grid non alignment to discontinuities with the major influence due to regulation of non convective diffusion the application is also experimented on schemes such as roe jameson schmidt turkel and some second order accurate methods the consistent improvement in accuracy either at moderate or marked levels for a variety of problems and with increasing grid size reasonably indicate a scope for ddr as a regular tool to impart genuine multidimensional upwinding effect in a simpler framework

optimal experimental design for another s analysis abstract we consider the optimal design of experiments in which estimation and design are performed by different parties the parties are assumed to share similar goals as reflected by a common loss function but they may have different prior beliefs after presenting a few motivating examples we examine the problem of optimal sample size selection under a normal likelihood with constant cost per observation we also consider the problem of optimal allocation for given overall sample sizes we present results under both squared error loss and a logarithmic utility paying attention to the differences between one and two prior optimal designs an asymmetric discrepancy measure features repeatedly in our development and we question the extent of its role in optimal two prior design

a robust bayesian interpretation of likelihood regions likelihood regions are shown to be robust in the sense that their posterior probability content is relatively insensitive to contaminations of the prior this provides a bayesian interpretation of regions that are commonly used by frequentists to construct confidence intervals and whose use are also advocated by the pure likelihood approach

global sensitivity results for generalized least squares estimates abstract the covariance matrix for the residuals of a regression process is written as the identity matrix plus a matrix v the matrix v is bounded from above and the corresponding set of generalized least squares estimates is identified the extreme estimates in this set are functions of the usual t statistics in particular the number t k 8 1 2 t measures the influence of reweighting extreme observations where t k gives the degrees of freedom t is the t statistic and the weights on observations are allowed to vary by a factor of at most 2

kernel search an application to the index tracking problem abstract in this paper we study the problem of replicating the performances of a stock market index i e the so called index tracking problem and the problem of out performing a market index i e the so called enhanced index tracking problem we introduce mixed integer linear programming milp formulations for these two problems furthermore we present a heuristic framework called kernel search we analyze and evaluate the behavior of several implementations of the kernel search framework to the solution of the index tracking problem we show the effectiveness and efficiency of the framework comparing the performances of these heuristics with those of a general purpose solver the computational experiments are carried out using benchmark and newly created instances

bayes optimal designs for two and three level factorial experiments abstract two and three level factorial designs are often used for exploratory experiments with many independent variables the purpose of such experiments is to estimate the effects of all active independent variables and their interactions for reasons of economy or other constraints only a fraction of the full number of experimental settings of the independent variables may be run precluding the separate data based estimation of all the effects in this situation of relatively sparse data and many unknown parameters the benefits of reliable prior information used in the estimation and experimental design can be especially significant in this article exact bayes optimal designs of two and three level fractional factorial experiments and of blocked two and three level factorial experiments are derived the optimality criteria used in this process are versions of the bayes criterion introduced by duncan and degroot it is shown that the classical fractional factorial designs for the 2k experime