convex extensions and envelopes of lower semi continuous functions we define a convex extension of a lower semi continuous function to be a convex function that is identical to the given function over a pre specified subset of its domain convex extensions are not necessarily constructible or unique we identify conditions under which a convex extension can be constructed when multiple convex extensions exist we characterize the tightest convex extension in a well defined sense using the notion of a generating set we establish conditions under which the tightest convex extension is the convex envelope then we employ convex extensions to develop a constructive technique for deriving convex envelopes of nonlinear functions finally using the theory of convex extensions we characterize the precise gaps exhibited by various underestimators of x y over a rectangle and prove that the extensions theory provides convex relaxations that are much tighter than the relaxation provided by the classical outer linearization of bilinear terms

identification of transport coefficient models in convection diffusion equations a rigorous method is presented for the systematic identification of the structure and the parameters of transport coefficient models in three dimensional transient convection diffusion systems using high resolution measurement data the transport is represented by a convection term with known convective velocity and a diffusion term with an unknown generally state dependent transport coefficient the identification of a transport coefficient model constitutes an ill posed highly nonlinear inverse problem in our previous work karalashvili et al siam j sci comput 30 2008 pp 3249 3269 we presented a novel incremental identification method which decomposes this inverse problem into easier to handle inverse subproblems this way the incremental identification method not only allows for the identification of the structure and the parameters of the model but also supports the rigorous decision making on the best suited transport model structure due to the decomposition approach the identified transport model structure and parameters are subject to errors to cope with the error propagation inherent in the incremental method the present work suggests a model correction procedure as a supplement to the incremental identification method of our previous work which results in a transport model of higher precision the correction refers to both the model structure and parameters no a priori knowledge on the unknown transport model structure is necessary the identification approach is numerically illustrated for a three dimensional transient convection diffusion equation which has its origin in the modeling and simulation of energy transport in a laminar wavy film flow

estimating propensity scores with missing covariate data using general location mixture models in many observational studies analysts estimate causal effects using propensity scores e g by matching sub classifying or inverse probability weighting based on the scores estimation of propensity scores is complicated when some values of the covariates are missing analysts can use multiple imputation to create completed data sets from which propensity scores can be estimated we propose a general location mixture model for imputations that assumes that the control units are a latent mixture of i units whose covariates are drawn from the same distributions as the treated units covariates and ii units whose covariates are drawn from different distributions this formulation reduces the influence of control units outside the treated units region of the covariate space on the estimation of parameters in the imputation model which can result in more plausible imputations in turn this can result in more reliable estimates of propensity scores and better balance in the true covariate distributions when matching or sub classifying we illustrate the benefits of the latent class modeling approach with simulations and with an observational study of the effect of breast feeding on children s cognitive abilities

an outer approximation algorithm for a class of mixed integer nonlinear programs an outer approximation algorithm is presented for solving mixed integer nonlinear programming problems of a particular class linearity of the integer or discrete variables and convexity of the nonlinear functions involving continuous variables are the main features in the underlying mathematical structure based on principles of decomposition outer approximation and relaxation the proposed algorithm effectively exploits the structure of the problems and consists of solving an alternating finite sequence of nonlinear programming subproblems and relaxed versions of a mixed integer linear master program convergence and optimality properties of the algorithm are presented as well as a general discussion on its implementation numerical results are reported for several example problems to illustrate the potential of the proposed algorithm for programs in the class addressed in this paper finally a theoretical comparison with generalized benders decomposition is presented on the lower bounds predicted by the relaxed master programs

stratification and weighting via the propensity score in estimation of causal treatment effects a comparative study estimation of treatment effects with causal interpretation from observational data is complicated because exposure to treatment may be confounded with subject characteristics the propensity score the probability of treatment exposure conditional on covariates is the basis for two approaches to adjusting for confounding methods based on stratification of observations by quantiles of estimated propensity scores and methods based on weighting observations by the inverse of estimated propensity scores we review popular versions of these approaches and related methods offering improved precision describe theoretical properties and highlight their implications for practice and present extensive comparisons of performance that provide guidance for practical use

a branch and cut algorithm for nonconvex quadratically constrained quadratic programming we present a branch and cut algorithm that yields in finite time a globally e optimal solution with respect to feasibility and optimality of the nonconvex quadratically constrained quadratic programming problem the idea is to estimate all quadratic terms by successive linearizations within a branching tree using reformulation linearization techniques rlt to do so four classes of linearizations cuts depending on one to three parameters are detailed for each class we show how to select the best member with respect to a precise criterion the cuts introduced at any node of the tree are valid in the whole tree and not only within the subtree rooted at that node in order to enhance the computational speed the structure created at any node of the tree is flexible enough to be used at other nodes computational results are reported that include standard test problems taken from the literature some of these problems are solved for the first time with a proof of global optimality

dual adaptive model predictive control abstract we present an adaptive dual model predictive controller dmpc that uses current and future parameter estimation errors to minimize expected output error by optimally combining probing for uncertainty reduction with control of the nominal model our novel approach relies on orthonormal basis function models to derive expressions for the predicted distributions for the output and unknown parameters conditional on the future input sequence propagating the exact future statistics enables reformulating the original stochastic problem into a deterministic equivalent that illustrates the dual nature of the optimal control but is nonlinear and nonconvex we further reformulate the nonlinear deterministic problem to pose an equivalent quadratically constrained quadratic programming qcqp problem that state of the art algorithms can solve efficiently providing the exact solution to the probabilistically constrained finite horizon dual control problem the adaptive dmpc solves this qcqp at each sampling time on a receding horizon the adaptation is a result of updating the parameter estimates used by the dmpc to decide the control input the paper demonstrates the application of dmpc to a single input single output siso system with unknown parameters in the simulation example the parameter estimates converge quickly and the probing vanishes with increasing accuracy and precision of the estimates improving the future control performance

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

an efficient global algorithm for single group multicast beamforming consider the single group multicast beamforming problem where multiple users receive the same data stream simultaneously from a single transmitter the problem is np hard and all existing algorithms for the problem either find suboptimal approximate or local stationary solutions in this paper we propose an efficient branch and bound algorithm for the problem that is guaranteed to find its global solution to the best of our knowledge our proposed algorithm is the first tailored global algorithm for the single group multicast beamforming problem simulation results show that our proposed algorithm is computationally efficient albeit its theoretical worst case iteration complexity is exponential with respect to the number of receivers and it significantly outperforms a state of the art general purpose global optimization solver called baron our proposed algorithm provides an important benchmark for performance evaluation of existing algorithms for the same problem by using it as the benchmark we show that two state of the art algorithms semidefinite relaxation algorithm and successive linear approximation algorithm work well when the problem dimension i e the number of antennas at the transmitter and the number of receivers is small but their performance deteriorates quickly as the problem dimension increases

adjusted kaplan meier estimator and log rank test with inverse probability of treatment weighting for survival data estimation and group comparison of survival curves are two very common issues in survival analysis in practice the kaplan meier estimates of survival functions may be biased due to unbalanced distribution of confounders here we develop an adjusted kaplan meier estimator akme to reduce confounding effects using inverse probability of treatment weighting iptw each observation is weighted by its inverse probability of being in a certain group the akme is shown to be a consistent estimate of the survival function and the variance of the akme is derived a weighted log rank test is proposed for comparing group differences of survival functions simulation studies are used to illustrate the performance of akme and the weighted log rank test the method proposed here outperforms the kaplan meier estimate and it does better than or as well as other estimators based on stratification the akme and the weighted log rank test are applied to two real examples one is the study of times to reinfection of sexually transmitted diseases and the other is the primary biliary cirrhosis pbc study

a global minlp approach to symbolic regression symbolic regression methods generate expression trees that simultaneously define the functional form of a regression model and the regression parameter values as a result the regression problem can search many nonlinear functional forms using only the specification of simple mathematical operators such as addition subtraction multiplication and division among others currently state of the art symbolic regression methods leverage genetic algorithms and adaptive programming techniques genetic algorithms lack optimality certifications and are typically stochastic in nature in contrast we propose an optimization formulation for the rigorous deterministic optimization of the symbolic regression problem we present a mixed integer nonlinear programming minlp formulation to solve the symbolic regression problem as well as several alternative models to eliminate redundancies and symmetries we demonstrate this symbolic regression technique using an array of experiments based upon literature instances we then use a set of 24 minlps from symbolic regression to compare the performance of five local and five global minlp solvers finally we use larger instances to demonstrate that a portfolio of models provides an effective solution mechanism for problems of the size typically addressed in the symbolic regression literature

on convex envelopes for bivariate functions over polytopes in this paper we discuss convex envelopes for bivariate functions satisfying suitable assumptions over polytopes we first propose a technique to compute the value and a supporting hyperplane of the convex envelope over a general two dimensional polytope through the solution of a three dimensional convex subproblem with continuously differentiable constraint functions then for quadratic functions as well as for some polynomial and rational ones again satisfying suitable assumptions we show how the same computations can be carried out through the solution of a single semidefinite problem

propensity score methods for bias reduction in the comparison of a treatment to a non randomized control group in observational studies investigators have no control over the treatment assignment the treated and non treated that is control groups may have large differences on their observed covariates and these differences can lead to biased estimates of treatment effects even traditional covariance analysis adjustments may be inadequate to eliminate this bias the propensity score defined as the conditional probability of being treated given the covariates can be used to balance the covariates in the two groups and therefore reduce this bias in order to estimate the propensity score one must model the distribution of the treatment indicator variable given the observed covariates once estimated the propensity score can be used to reduce bias through matching stratification subclassification regression adjustment or some combination of all three in this tutorial we discuss the uses of propensity score methods for bias reduction give references to the literature and illustrate the uses through applied examples

missing covariates in generalized linear models when the missing data mechanism is non ignorable we propose a method for estimating parameters in generalized linear models with missing covariates and a non ignorable missing data mechanism we use a multinomial model for the missing data indicators and propose a joint distribution for them which can be written as a sequence of one dimensional conditional distributions with each one dimensional conditional distribution consisting of a logistic regression we allow the covariates to be either categorical or continuous the joint covariate distribution is also modelled via a sequence of one dimensional conditional distributions and the response variable is assumed to be completely observed we derive the e and m steps of the em algorithm with non ignorable missing covariate data for categorical covariates we derive a closed form expression for the e and m steps of the em algorithm for obtaining the maximum likelihood estimates mles for continuous covariates we use a monte carlo version of the em algorithm to obtain the mles via the gibbs sampler computational techniques for gibbs sampling are proposed and implemented the parametric form of the assumed missing data mechanism itself is not testable from the data and thus the non ignorable modelling considered here can be viewed as a sensitivity analysis concerning a more complicated model therefore although a model may have passed the tests for a certain missing data mechanism this does not mean that we have captured even approximately the correct missing data mechanism hence model checking for the missing data mechanism and sensitivity analyses play an important role in this problem and are discussed in detail several simulations are given to demonstrate the methodology in addition a real data set from a melanoma cancer clinical trial is presented to illustrate the methods proposed

optimization as an analysis tool for human complex problem solving we present a problem class of mixed integer nonlinear programs minlps with nonconvex continuous relaxations which stem from economic test scenarios that are used in the analysis of human complex problem solving in a round based scenario participants hold an executive function a posteriori a performance indicator is calculated and correlated to personal measures such as intelligence working memory or emotion regulation altogether we investigate 2088 optimization problems that differ in size and initial conditions based on real world experimental data from 12 rounds of 174 participants the goals are twofold first from the optimal solutions we gain additional insight into a complex system which facilitates the analysis of a participant s performance in the test second we propose a methodology to automatize this process by providing a new criterion based on the solution of a series of optimization problems by providing a mathematical optimization model and this methodology we disprove the ass

estimating and using propensity scores with partially missing data abstract investigators in observational studies have no control over treatment assignment as a result large differences can exist between the treatment and control groups on observed covariates which can lead to badly biased estimates of treatment effects propensity score methods are an increasingly popular method for balancing the distribution of the covariates in the two groups to reduce this bias for example using matching or subclassification sometimes in combination with model based adjustment to estimate propensity scores which are the conditional probabilities of being treated given a vector of observed covariates we must model the distribution of the treatment indicator given these observed covariates much work has been done in the case where covariates are fully observed we address the problem of calculating propensity scores when covariates can have missing values in such cases which commonly arise in practice the pattern of missing covariates can be prognostically important and

explicit convex and concave envelopes through polyhedral subdivisions in this paper we derive explicit characterizations of convex and concave envelopes of several nonlinear functions over various subsets of a hyper rectangle these envelopes are obtained by identifying polyhedral subdivisions of the hyper rectangle over which the envelopes can be constructed easily in particular we use these techniques to derive in closed form the concave envelopes of concave extendable supermodular functions and the convex envelopes of disjunctive convex functions

on minimal valid inequalities for mixed integer conic programs we study disjunctive conic sets involving a general regular closed convex full dimensional and pointed cone x1d4a6 such as the nonnegative orthant the lorentz cone or the positive semidefinite cone in a unified framework we introduce x1d4a6 minimal inequalities and show that under mild assumptions these inequalities together with the trivial cone implied inequalities are sufficient to describe the convex hull we focus on the properties of x1d4a6 minimal inequalities by establishing algebraic necessary conditions for an inequality to be x1d4a6 minimal this characterization leads to a broader algebraically defined class of x1d4a6 sublinear inequalities we demonstrate a close connection between x1d4a6 sublinear inequalities and the support functions of convex sets with a particular structure this connection results in practical ways of verifying x1d4a6 sublinearity and or x1d4a6 minimality of inequalities our study generalizes some of the results from the mixed integer linear case it is well known that the minimal inequalities for

exact quadratic convex reformulations of mixed integer quadratically constrained problems we propose a solution approach for the general problem qp of minimizing a quadratic function of bounded integer variables subject to a set of quadratic constraints the resolution is based on the reformulation of the original problem qp into an equivalent quadratic problem whose continuous relaxation is convex so that it can be effectively solved by a branch and bound algorithm based on quadratic convex relaxation we concentrate our efforts on finding a reformulation such that the continuous relaxation bound of the reformulated problem is as tight as possible furthermore we extend our method to the case of mixed integer quadratic problems with the following restriction all quadratic sub functions of purely continuous variables are already convex finally we illustrate the different results of the article by small examples and we present some computational experiments on pure integer and mixed integer instances of qp most of the considered instances with up to 53 variables can be solved by our approach combined with the use of cplex

mccormick based relaxations of algorithms theory and implementation for the global optimization of a wide class of algorithms is presented via convex affine relaxations the basis for the proposed relaxations is the systematic construction of subgradients for the convex relaxations of factorable functions by mccormick math prog 10 1976 pp 147 175 similar to the convex relaxation the subgradient propagation relies on the recursive application of a few rules namely the calculation of subgradients for addition multiplication and composition operations subgradients at interior points can be calculated for any factorable function for which a mccormick relaxation exists provided that subgradients are known for the relaxations of the univariate intrinsic functions for boundary points additional assumptions are necessary an automated implementation based on operator overloading is presented and the calculation of bounds based on affine relaxation is demonstrated for illustrative examples two numerical examples for the global optimization of algorithms are presented in both examples a parameter estimation problem with embedded differential equations is considered the solution of the differential equations is approximated by algorithms with a fixed number of iterations

strong socp relaxations for the optimal power flow problem this paper proposes three strong second order cone programming socp relaxations for the ac optimal power flow opf problem these three relaxations are incomparable to each other and two of them are incomparable to the standard sdp relaxation of opf extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in the literature i their solution quality is extremely close to that of the standard sdp relaxation the best one is within 99 96 of the sdp relaxation on average for all the ieee test cases and consistently outperforms previously proposed convex quadratic relaxations of the opf problem ii the solutions from the strong socp relaxations can be directly used as a warm start in a local solver such as ipopt to obtain a high quality feasible opf solution and iii in terms of computation times the strong socp relaxations can be solved an order of magnitude faster than the standard sdp relaxation for example one of the proposed s

approximation of the least rayleigh quotient for degree p homogeneous functionals abstract we present two novel methods for approximating minimizers of the abstract rayleigh quotient u u p here is a strictly convex functional on a banach space with norm and is assumed to be positively homogeneous of degree p 1 minimizers are shown to satisfy u j p u 0 for a certain r where j p is the subdifferential of 1 p p the first approximation scheme is based on inverse iteration for square matrices and involves sequences that satisfy u k j p u k 1 0 k n the second method is based on the large time behavior of solutions of the doubly nonlinear evolution j p v t v t 0 a e t 0 and more generally p curves of maximal slope for we show that both schemes have the remarkable property that the rayleigh quotient is nonincreasing along solutions and that properly scaled solutions converge to a minimizer of u u p these results are new even for hilbert spaces and their primary application is in the approximation of optimal constants and extremal functions for inequalities in sobolev spaces

error bounds for monomial convexification in polynomial optimization convex hulls of monomials have been widely studied in the literature and monomial convexifications are implemented in global optimization software for relaxing polynomials however there has been no study of the error in the global optimum from such approaches we give bounds on the worst case error for convexifying a monomial over subsets of this implies additive error bounds for relaxing a polynomial optimization problem by convexifying each monomial separately our main error bounds depend primarily on the degree of the monomial making them easy to compute since monomial convexification studies depend on the bounds on the associated variables in the second part we conduct an error analysis for a multilinear monomial over two different types of box constraints as part of this analysis we also derive the convex hull of a multilinear monomial over

propensity score estimation with missing values using a multiple imputation missingness pattern mimp approach propensity scores have been used widely as a bias reduction method to estimate the treatment effect in nonrandomized studies since many covariates are generally included in the model for estimating the propensity scores the proportion of subjects with at least one missing covariate could be large while many methods have been proposed for propensity score based estimation in the presence of missing covariates little has been published comparing the performance of these methods in this article we propose a novel method called multiple imputation missingness pattern mimp and compare it with the naive estimator ignoring propensity score and three commonly used methods of handling missing covariates in propensity score based estimation separate estimation of propensity scores within each pattern of missing data multiple imputation and discarding missing data under different mechanisms of missing data and degree of correlation among covariates simulation shows that all adjusted estimators are much less biased than the naive estimator under certain conditions mimp provides benefits smaller bias and mean squared error compared with existing alternatives

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

mathematical programming techniques in water network optimization abstract in this article we survey mathematical programming approaches to problems in the field of drinking water distribution network optimization among the predominant topics treated in the literature we focus on two different but related problem classes one can be described by the notion of network design while the other is more aptly termed by network operation the basic underlying model in both cases is a nonlinear network flow model and we give an overview on the more specific modeling aspects in each case the overall mathematical model is a mixed integer nonlinear program having a common structure with respect to how water dynamics in pipes are described finally we survey the algorithmic approaches to solve the proposed problems and we discuss computation on various types of water networks

a polyhedral branch and cut approach to global optimization a variety of nonlinear including semidefinite relaxations have been developed in recent years for nonconvex optimization problems their potential can be realized only if they can be solved with sufficient speed and reliability unfortunately state of the art nonlinear programming codes are significantly slower and numerically unstable compared to linear programming software in this paper we facilitate the reliable use of nonlinear convex relaxations in global optimization via a polyhedral branch and cut approach our algorithm exploits convexity either identified automatically or supplied through a suitable modeling language construct in order to generate polyhedral cutting planes and relaxations for multivariate nonconvex problems we prove that if the convexity of a univariate or multivariate function is apparent by decomposing it into convex subexpressions our relaxation constructor automatically exploits this convexity in a manner that is much superior to developing polyhedral outer approximators for the original function the convexity of functional expressions that are composed to form nonconvex expressions is also automatically exploited root node relaxations are computed for 87 problems from globallib and minlplib and detailed computational results are presented for globally solving 26 of these problems with baron 7 2 which implements the proposed techniques the use of cutting planes for these problems reduces root node relaxation gaps by up to 100 and expedites the solution process often by several orders of magnitude

integer programming subject to monomial constraints we investigate integer programs containing constraints of the type prod i in i x i alpha i b due to the number theoretic nature of these constraints standard methods based on linear algebra cannot be applied directly instead we present a reformulation resulting in integer programs with linear constraints and polynomial objective functions using prime decompositions of the right hand sides b moreover we show that minimizing a linear objective function with nonnegative coefficients over bivariate constraints is possible in polynomial time

a milp formulation for generalized geometric programming using piecewise linear approximations abstract generalized geometric programming ggp problems are converted to mixed integer linear programming milp problems using piecewise linear approximations our approach is to approximate a multiple term log sum function of the form log x 1 x 2 x n in terms of a set of linear equalities or inequalities of log x 1 log x 2 and log x n where x 1 x n are strictly positive the advantage of this approach is its simplicity and readiness to implement and solve using commercial milp solvers while milp problems in general are no easier than ggp problems this approach is justified by the phenomenal progress of computing power of both personal computers and commercial milp solvers the limitation of this approach is discussed along with numerical tests

polyhedral approximation in mixed integer convex optimization generalizing both mixed integer linear optimization and convex optimization mixed integer convex optimization possesses broad modeling power but has seen relatively few advances in general purpose solvers in recent years in this paper we intend to provide a broadly accessible introduction to our recent work in developing algorithms and software for this problem class our approach is based on constructing polyhedral outer approximations of the convex constraints resulting in a global solution by solving a finite number of mixed integer linear and continuous convex subproblems the key advance we present is to strengthen the polyhedral approximations by constructing them in a higher dimensional space in order to automate this extended formulation we rely on the algebraic modeling technique of disciplined convex programming dcp and for generality and ease of implementation we use conic representations of the convex constraints although our framework requires a manual translation of existing models into dcp form after performing this transformation on the minlplib2 benchmark library we were able to solve a number of unsolved instances and on many other instances achieve superior performance compared with state of the art solvers like bonmin scip and artelys knitro

global optimization in hilbert space we propose a complete search algorithm for solving a class of non convex possibly infinite dimensional optimization problems to global optimality we assume that the optimization variables are in a bounded subset of a hilbert space and we determine worst case run time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set because these run time bounds are independent of the number of optimization variables and in particular are valid for optimization problems with infinitely many optimization variables we prove that the algorithm converges to an varepsilon suboptimal global solution within finite run time for any given termination tolerance varepsilon 0 finally we illustrate these results for a problem of calculus of variations

global optimization of mixed integer nonlinear programs a theoretical and computational study this work addresses the development of an efficient solution strategy for obtaining global optima of continuous integer and mixed integer nonlinear programs towards this end we develop novel relaxation schemes range reduction tests and branching strategies which we incorporate into the prototypical branch and bound algorithm in the theoretical algorithmic part of the paper we begin by developing novel strategies for constructing linear relaxations of mixed integer nonlinear programs and prove that these relaxations enjoy quadratic convergence properties we then use lagrangian linear programming duality to develop a unifying theory of domain reduction strategies as a consequence of which we derive many range reduction strategies currently used in nonlinear programming and integer linear programming this theory leads to new range reduction schemes including a learning heuristic that improves initial branching decisions by relaying data across siblings in a branch and bound tree finally we incorporate these relaxation and reduction strategies in a branch and bound algorithm that incorporates branching strategies that guarantee finiteness for certain classes of continuous global optimization problems in the computational part of the paper we describe our implementation discussing wherever appropriate the use of suitable data structures and associated algorithms we present computational experience with benchmark separable concave quadratic programs fractional 0 1 programs and mixed integer nonlinear programs from applications in synthesis of chemical processes engineering design just in time manufacturing and molecular design

robust goal programming using different robustness echelons via norm based and ellipsoidal uncertainty sets abstract the notion of robust goal programming rgp using cardinality constrained robustness via interval based uncertainty was first examined over a decade ago since then the rgp methodology has not been widely researched specifically when considering different uncertainty sets to implement within this context this paper compares interval based and norm based uncertainty sets using cardinality constrained robustness strict robustness using ellipsoidal uncertainty sets is also examined in the rgp realm the aforementioned methods are demonstrated for a simple instance from the literature and the results are summarized conclusions are made regarding the proposed rgp models when likened to a similar rgp model seen in the literature further the suitability of each rgp model is offered when a decision maker s risk preference or computing availability are taken into consideration inferences are made regarding the effectiveness of each uncertainty set in the context of solutions that are relatively unaffected by data uncertainty that is robust solutions

model based direct adjustment abstract direct adjustment or standardization applies population weights to subclass means in an effort to estimate population quantities from a sample that is not representative of the population direct adjustment has several attractive features but when there are many subclasses it can attach large weights to small quantities of data often in a fairly erratic manner in the extreme direct adjustment can attach infinite weight to nonexistent data a noticeable inconvenience in practice this article proposes a method of model based direct adjustment that preserves the attractive features of conventional direct adjustment while stabilizing the weights attached to small subclasses the sample mean and conventional direct adjustment are both special cases of model based direct adjustment under two different extreme models for the subclass specific selection probabilities the discussion of this method provides some insights into the behavior of true and estimated propensity scores the estimated scores

causal inference with confounders missing not at random author s yang s wang l ding p abstract 2019 biometrika trust it is important to draw causal inference from observational studies but this becomes challenging if the confounders have missing values generally causal effects are not identifiable if the confounders are missing not at random in this article we propose a novel framework for nonparametric identification of causal effects with confounders subject to an outcome independent missingness which means that the missing data mechanism is independent of the outcome given the treatment and possibly missing confounders we then propose a nonparametric two stage least squares estimator and a parametric estimator for causal effects

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

conic mixed integer rounding cuts a conic integer program is an integer programming problem with conic constraints many problems in finance engineering statistical learning and probabilistic optimization are modeled using conic constraints here we study mixed integer sets defined by second order conic constraints we introduce general purpose cuts for conic mixed integer programming based on polyhedral conic substructures of second order conic sets these cuts can be readily incorporated in branch and bound algorithms that solve either second order conic programming or linear programming relaxations of conic integer programs at the nodes of the branch and bound tree central to our approach is a reformulation of the second order conic constraints with polyhedral second order conic constraints in a higher dimensional space in this representation the cuts we develop are linear even though they are nonlinear in the original space of variables this feature leads to a computationally efficient implementation of nonlinear cuts for conic mixed integer programming the reformulation also allows the use of polyhedral methods for conic integer programming we report computational results on solving unstructured second order conic mixed integer problems as well as mean variance capital budgeting problems and least squares estimation problems with binary inputs our computational experiments show that conic mixed integer rounding cuts are very effective in reducing the integrality gap of continuous relaxations of conic mixed integer programs and hence improving their solvability