For the purpose of causal inference we employ a stochastic model of the data generating process, utilizing individual propensity probabilities for the treatment, and also individual and counterfactual prognosis probabilities for the outcome. We assume a generalized version of the stable unit treatment value assumption, but we do not assume any version of strongly ignorable treatment assignment. Instead of conducting a sensitivity analysis, we utilize the principle of maximum entropy to estimate the distribution of causal effects. We develop a principled middle-way between extreme explanations of the observed data: we do not conclude that an observed association is wholly spurious, and we do not conclude that it is wholly causal. Rather, our conclusions are tempered and we conclude that the association is part spurious and part causal. In an example application we apply our methodology to analyze an observed association between marijuana use and hard drug use.

It can be difficult to interpret a coefficient of an uncertain model. A slope coefficient of a regression model may change as covariates are added or removed from the model. In the context of high-dimensional data, there are too many model extensions to check. However, as we show here, it is possible to efficiently search, with a branch and bound algorithm, for maximum and minimum values of that adjusted slope coefficient over a discrete space of regularized regression models. Here we introduce our algorithm, along with supporting mathematical results, an example application, and a link to our computer code, to help researchers summarize high-dimensional data and assess the stability of regression coefficients in uncertain models.

In generalized pattern search algorithms for linearly constrained optimization, certain limit points have been shown to satisfy a pseudo-second-order necessary condition, in which positive semidefiniteness of the Hessian is achieved only with respect to an orthonormal basis. Satisfaction of the full second-order condition can only be ensured if the finite set of positive spanning directions includes the eigenvectors of the Hessian at the limit point. Of course, this is generally not possible in practice, due to the unavailability of derivatives. The present work takes advantage of a chief feature of the more general parent class of generating set search algorithms – that of allowing the use of an infinite (non-dense) set of directions in the limit. If approximate second derivative information is gathered during the iteration process, then the normalized eigenvectors of the approximate Hessian can be used to construct the set of 2n orthonormal directions used by the algorithm. If the Hessian approximation converges in the limit to the true Hessian (or a matrix in the generalized Hessian), then the full second-order optimality conditions can be achieved. Two approaches for generating such a convergent approximate Hessian are described. Numerical examples show the effectiveness of the approach.

In this paper, we characterize a new class of computationally expensive optimization problems and introduce an approach for solving them. In this class of problems, objective function values may be directly related to the computational time required to obtain them, so that, as the optimal solution is approached, the computational time required to evaluate the objective is significantly less than at points farther away from the solution. This is motivated by an application in which each objective function evaluation requires both a numerical fluid dynamics simulation and an image registration process, and the goal is to find the parameter values of a predetermined reference image by comparing the flow dynamics from the numerical simulation and the reference image through the image comparison process. In designing an approach to numerically solve the more general class of problems in an efficient way, we make use of surrogates based on CPU times of previously evaluated points, rather than their function values, all within the search step framework of mesh adaptive direct search algorithms. Because of the expected positive correlation between function values and their CPU times, a time cutoff parameter is added to the objective function evaluation to allow its termination during the comparison process if the computational time exceeds a specified threshold. The approach was tested using the NOMADm and DACE MATLAB® software packages, and results are presented.

In this paper, we examine how to improve the frequency and accuracy with which highquality Earth observations are made by coordinating across multiple collection systems, including air and space assets, in an asynchronous environment. In particular, we consider how these improvements could impact Earth observing sensors in two use areas; climate studies and intelligence collection operations. To do this, we make simplifying but reasonable assumptions and use a complex yet intuitive value function to solve a series of simple optimization problems that allocate requests to single-mission planners, or “sub-planners.” We consider requests with time windows and priority levels, some of which require simultaneous observations by different sensors. The primary contributions of this paper include our approach to the asynchronous and distributed nature of the problem and the development of a value function to facilitate the coordination of the observations with multiple surveillance assets.

As a model for streaming multimedia applications, we study an unreliable retrial queue with infinite-capacity orbit and normal queue for which the retrial rate and the server repair rate are controllable. Customers join the retrial orbit if and only if their service is interrupted by a server failure. Interrupted customers do not rejoin the normal queue but repeatedly attempt to access the server at independent and identically distributed intervals until it is found functioning and idle. We provide stability conditions, queue length distributions, stochastic decomposition results, and performance measures. The joint optimization of the retrial and server repair rates is also studied.

The purpose of this paper is to introduce a new way of choosing directions for the mesh adaptive direct search (Mads) class of algorithms. The advantages of this new OrthoMads instantiation of Mads are that the polling directions are chosen deterministically, ensuring that the results of a given run are repeatable, and that they are orthogonal to each other, which yields convex cones of missed directions at each iteration that are minimal in a reasonable measure. Convergence results for OrthoMads follow directly from those already published for Mads, and they hold deterministically, rather than with probability one, as is the case for LtMads, the first Mads instance. The initial numerical results are quite good for both smooth and nonsmooth and constrained and unconstrained problems considered here.

This paper introduces a new approach to the problem of quantitative reconstruction of an object from few radiographic views. A mixed variable programming problem is formulated in which the variables of interest are the number and types of materials and geometric parameters. To demonstrate the technique, we considered the problem of reconstructing cylindrically symmetric objects of multiple layers from a single radiograph. The mixed variable pattern search algorithm for linearly constrained problems was applied by means of the NOMADm MATLAB software package. Numerical results are presented for several test configurations and show that, while there are difficulties yet to be overcome, the method is promising for solving this class of problems.

This paper deals with generalized pattern search (GPS) algorithms for linearly constrained optimization. At each iteration, the GPS algorithm generates a set of directions that conforms to the geometry of any nearby linear constraints. This set is then used to construct trial points to be evaluated during the iteration. In a previous work, Lewis and Torczon developed a scheme for computing the conforming directions, however, the issue of degeneracy merits further investigation. The contribution of this paper is to provide a detailed algorithm for constructing the set of directions whether or not the constraints are degenerate. One difficulty in the degenerate case is the classification of constraints as redundant or nonredundant. We give a short survey of the main definitions and methods for treating redundancy and propose an approach to identify nonredundant ϵ-active constraints. We also introduce a new approach for handling nonredundant linearly dependent constraints, which maintains GPS convergence properties without significantly increasing computational cost. Some simple numerical tests illustrate the effectiveness of the algorithm.

In this paper, we characterize a new class of optimization problems in which objective function values are correlated with the computational time required to obtain these values. That is, as the optimal solution is approached, the computational time required to compute an objective function values decreases significantly. This is mo- tivated by an application in which each objective function evaluation requires both a numerical fluid dynamics simulation and an image registration process, and the goal is to find the parameter values of a predetermined reference image by comparing the flow dynamics from the numerical simulation and the reference image through the image comparison process. In designing an approach to numerically solve the more general class of problems in an efficient way, we make use of surrogates based on CPU times of previously evaluated points, rather than their function values, all within the search step framework of mesh adaptive direct search algorithms. Because of the expected CPU time correlation, a time cutoff parameter was added to the objective function evaluation to allow its termination during the comparison process if the computational time exceeds a specified threshold. The approach was tested using the NOMADm and DACE MATLABr software packages, and results are presented.

δ Injection angle N Number of injectors Nmax Maximum number of injectors PT Jet total pressure (psia) TT Jet total temperature (R) y1 Axial distance to combustor half-line penetration y2 Axial distance to adjacent plume merge y3 Axial distance to stoichiometric fuel concentration decay d∗ Injector diameter (inches) w Combustor width (inches) fST Stoichiometric fuel-air ratio Subscript i Performance measure number j Mach number

The class of generalized pattern search (GPS) algorithms for mixed variable optimization is extended to problems with stochastic objective functions. Because random noise in the objective function makes it more difficult to compare trial points and ascertain which points are truly better than others, replications are needed to generate sufficient statistical power to draw conclusions. Rather than comparing pairs of points, the approach taken here augments pattern search with a ranking and selection (R&S) procedure, which allows for comparing many function values simultaneously. Asymptotic convergence for the algorithm is established, numerical issues are discussed, and performance of the algorithm is studied on a set of test problems.

This paper introduces a new derivative-free class of mesh adaptive direct search (MADS) algorithms for solving constrained mixed variable optimization problems, in which the variables may be continuous or categorical. This new class of algorithms, called mixed variable MADS (MV-MADS), generalizes both mixed variable pattern search (MVPS) algorithms for linearly constrained mixed variable problems and MADS algorithms for general constrained problems with only continuous variables. The convergence analysis, which makes use of the Clarke nonsmooth calculus, similarly generalizes the existing theory for both MVPS and MADS algorithms, and reasonable conditions are established for ensuring convergence of a subsequence of iterates to a suitably defined stationary point in the nonsmooth and mixed variable sense.

This paper deals with generalized pattern search (GPS) algorithms for linearly constrained optimization. At each iteration, the GPS algorithm generates a set of directions that conforms to the geometry of any nearby linear constraints. This set is then used to construct trial points to be evaluated during the iteration. In previous work, Lewis and Torczon developed a scheme for computing the conforming directions; however, the issue of degeneracy merits further investigation. The contribution of this paper is to provide a detailed algorithm for constructing the set of directions whether or not the constraints are degenerate. One difficulty in the degenerate case is in classifying constraints as redundant or nonredundant. We give a short survey of the main definitions and methods for treating redundancy and propose an approach to identify nonredundant ε-active constraints, which may be useful for other active set algorithms. We also introduce a new approach for handling nonredundant linearly dependent constraints, which maintains GPS convergence properties without significantly increasing computational cost. Some simple numerical tests illustrate the effectiveness of the algorithm. We conclude by briefly considering the extension of our ideas to nonlinear constrained optimization in which constraint gradients are linearly dependent.

Abstract : Researchers in many fields often need to quantify the similarity between images using metrics that measure qualities of interest in a robust quantitative manner. We present here the concept of image dimension reduction through characteristic shape sequences. We formulate the problem as a nonlinear optimization program and demonstrate the solution on a test problem of extracting maximal area ellipses from two dimensional image data. To solve the problem numerically, we augment the class of mesh adaptive direct search (MADS) algorithms with a filter, so as to allow infeasible starting points and to achieve better local solutions. Results here show that the MADS filter algorithm is successful in the test problem of finding good characteristic ellipse solutions from simple but noisy images.

A previous analysis of second-order behavior of generalized pattern search algorithms for unconstrained and linearly constrained minimization is extended to the more general class of mesh adaptive direct search ( MADS) algorithms for general constrained optimization. Because of the ability of MADS to generate an asymptotically dense set of search directions, we are able to establish reasonable conditions under which a subsequence of MADS iterates converges to a limit point satisfying second-order necessary or sufficient optimality conditions for general set-constrained optimization problems.

This paper is intended not as a survey, but as an introduction to some ideas behind the class of mesh adaptive direct search (MADS) methods. Space limitations dictate a brief description of various key topics to be provided along with several references, which themselves provide further references. The convergence theory for the methods presented here make a case for closing the gap between nonlinear optimizers and nonsmooth analysts. However these methods are certainly not of purely theoretical interest; they are successful on difficult practical problems. To encourage further use, we give references to available implementations. MADS is implemented in the direct search portion of the MathWorks MATLAB Genetic Algorithm and Direct Search (GADS) Toolbox.

: This paper is intended not as a survey, but as an introduction to some ideas behind the class of mesh adaptive direct search (MADS) methods. Space limitations dictate a brief description of various key topics to be provided along with several references, which themselves provide further references. The convergence theory for the methods presented here make a case for closing the gap between nonlinear optimizers and nonsmooth analysts. However these methods are certainly not of purely theoretical interest; they are successful on difficult practical problems. To encourage further use, we give references to available implementations. MADS is implemented in the direct search portion of the MathWorks MATLAB Genetic Algorithm and Direct Search (GADS) Toolbox.