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Development and Application of the Collaborative Optimization Architecture in a Multidisciplinary Design Environment
 Multidisciplinary Design Optimization: State of the Art
, 1996
"... Collaborative optimization is a design architecture applicable in any multidisciplinary analysis environment but specifically intended for largescale distributed analysis applications. In this approach, a complex problem is hierarchically decomposed along disciplinary boundaries into a number of su ..."
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Cited by 30 (3 self)
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Collaborative optimization is a design architecture applicable in any multidisciplinary analysis environment but specifically intended for largescale distributed analysis applications. In this approach, a complex problem is hierarchically decomposed along disciplinary boundaries into a number of subproblems which are brought into multidisciplinary agreement by a systemlevel coordination process. When applied to problems in a multidisciplinary design environment, this scheme has several advantages over traditional solution strategies. These advantageous features include reducing the amount of information transferred between disciplines, the removal of large iterationloops, allowing the use of different subspace optimizers among the various analysis groups, an analysis framework which is easily parallelized and can operate on heterogenous equipment, and a structural framework that is wellsuited for conventional disciplinary organizations. In this article, the collaborative architectu...
Efficient Estimation for the Cox Model with Interval Censoring
 Annals of Statistics
, 1996
"... The maximum likelihood estimator (MLE) for the proportional hazards model with current status data is studied. It is shown that the MLE for the regression parameter is asymptotically normal with p nconvergence rate and achieves the information bound, even though the MLE for the baseline cumulativ ..."
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Cited by 29 (6 self)
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The maximum likelihood estimator (MLE) for the proportional hazards model with current status data is studied. It is shown that the MLE for the regression parameter is asymptotically normal with p nconvergence rate and achieves the information bound, even though the MLE for the baseline cumulative hazard function only converges at n 1=3 rate. Estimation of the asymptotic variance matrix for the MLE of the regression parameter is also considered. To prove our main results, we also establish a general theorem showing that the MLE of the finite dimensional parameter in a class of semiparametric models is asymptotically efficient even though the MLE of the infinite dimensional parameter converges at a rate slower than p n. The results are illustrated by applying them to a data set from a tumoriginicity study. 1. Introduction In many survival analysis problems, we are interested in the relationship between a failure time T and a vector of covariates Z. However, it is common that obs...
Theory and implementation of numerical methods based on RungeKutta integration for solving optimal control problems
, 1996
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Interactive PhysicallyBased Manipulation of Discrete/Continuous Models
, 1995
"... Physicallybased modeling has been used in the past to support a variety of interactive modeling tasks including freeform surface design, mechanism design, constrained drawing, and interactive camera control. In these systems, the user interacts with the model by exerting virtual forces, to which t ..."
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Cited by 24 (1 self)
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Physicallybased modeling has been used in the past to support a variety of interactive modeling tasks including freeform surface design, mechanism design, constrained drawing, and interactive camera control. In these systems, the user interacts with the model by exerting virtual forces, to which the system responds subject to the active constraints. In the past, this kind of interaction has been applicable only to models that are governed by continuous parameters. In this paper we present an extension to mixed continuous /discrete models, emphasizing constrained layout problems that arise in architecture and other domains. When the object being dragged is blocked from further motion by geometric constraints, a local discrete search is triggered, during which transformations such as swapping of adjacent objects may be performed. The result of the search is a "nearby" state in which the target object has been moved in the indicated direction and in which all constraints are satisfied. ...
Analysis and implementation of a dual algorithm for constrained optimization
 Journal of Optimization Theory and Applications
, 1993
"... Abstract. This paper analyzes a constrained optimization algorithm that combines an unconstrained minimization scheme like the conjugate gradient method, an augmented Lagrangian, and multiplier updates to obtain global quadratic convergence. Some of the issues that we focus on are the treatment of r ..."
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Cited by 19 (3 self)
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Abstract. This paper analyzes a constrained optimization algorithm that combines an unconstrained minimization scheme like the conjugate gradient method, an augmented Lagrangian, and multiplier updates to obtain global quadratic convergence. Some of the issues that we focus on are the treatment of rigid constraints that must be satisfied during the iterations and techniques for balancing the error associated with constraint violation with the error associated with optimality. A preconditioner is constructed with the property that the rigid constraints are satisfied while illconditioning due to penalty terms is alleviated. Various numerical linear algebra techniques required for the efficient implementation of the algorithm are presented, and convergence behavior is illustrated in a series of numerical experiments.
Use Of The Collaborative Optimization Architecture For Launch Vehicle Design
 6th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
, 1996
"... Collaborative optimization is a new design architecture specifically created for largescale distributedanalysis applications. In this approach, a problem is decomposed into a userdefined number of subspace optimization problems that are driven towards interdisciplinary compatibility and the appro ..."
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Cited by 18 (1 self)
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Collaborative optimization is a new design architecture specifically created for largescale distributedanalysis applications. In this approach, a problem is decomposed into a userdefined number of subspace optimization problems that are driven towards interdisciplinary compatibility and the appropriate solution by a systemlevel coordination process. This decentralized design strategy allows domainspecific issues to be accommodated by disciplinary analysts, while requiring interdisciplinary decisions to be reached by consensus. The present investigation focuses on application of the collaborative optimization architecture to the multidisciplinary design of a singlestagetoorbit launch vehicle. Vehicle design, trajectory, and cost issues are directly modeled. Posed to suit the collaborative architecture, the design problem is characterized by 95 design variables and 16 constraints. Numerous collaborative solutions are obtained. Comparison of these solutions demonstrates the influe...
The Equivalence of Constrained and Weighted Designs in Multiple Objective Design Problems
 Journal of the American Statistical Association
, 1996
"... Several competing objectives may be relevant in the design of an experiment. The competing objectives may not be easy to characterize in a single optimality criterion. One approach to these design problems has been to weight each criterion and find the design that optimizes the weighted average of t ..."
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Cited by 16 (3 self)
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Several competing objectives may be relevant in the design of an experiment. The competing objectives may not be easy to characterize in a single optimality criterion. One approach to these design problems has been to weight each criterion and find the design that optimizes the weighted average of the criteria. An alternative approach has been to optimize one criterion subject to constraints on the other criteria. An equivalence theorem is presented for the Bayesian constrained design problem. Equivalence theorems are essential in verifying optimality of proposed designs, especially when, as in most nonlinear design problems, numerical optimization is required. This theorem is used to show that the results of Cook and Wong on the equivalence of the weighted and constrained problems also apply much more generally. The results are applied to Bayesian nonlinear design problems with several objectives. KEY WORDS: Bayesian design, regression, nonlinear design 1. INTRODUCTION An experimen...
User’s Guide for SNOPT Version 7: Software for LargeScale Nonlinear Programming
"... SNOPT is a generalpurpose system for constrained optimization. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for largescale linear and quadratic programming and for linearly constrained optimization, as wel ..."
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Cited by 16 (0 self)
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SNOPT is a generalpurpose system for constrained optimization. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for largescale linear and quadratic programming and for linearly constrained optimization, as well as for general nonlinear programs. SNOPT finds solutions that are locally optimal, and ideally any nonlinear functions should be smooth and users should provide gradients. It is often more widely useful. For example, local optima are often global solutions, and discontinuities in the function gradients can often be tolerated if they are not too close to an optimum. Unknown gradients are estimated by finite differences. SNOPT uses a sequential quadratic programming (SQP) algorithm. Search directions are obtained from QP subproblems that minimize a quadratic model of the Lagrangian function subject to linearized constraints. An augmented Lagrangian merit function is reduced along each search direction to ensure convergence from any starting point.
The TOMLAB Graphical User Interface for Nonlinear Programming. Advanced Modeling and Optimization
 in MATLAB. Annals of Operations Research, Modeling Languages and Approaches: Submitted
, 1999
"... The paper presents a Graphical User Interface (GUI) for nonlinear programming in Matlab. The GUI gives easy access to all features in the NLPLIB TB (NonLinear Programming LIBrary Toolbox) � a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrain ..."
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Cited by 13 (9 self)
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The paper presents a Graphical User Interface (GUI) for nonlinear programming in Matlab. The GUI gives easy access to all features in the NLPLIB TB (NonLinear Programming LIBrary Toolbox) � a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrained optimization, quadratic programming, unconstrained and constrained nonlinear least squares, boxbounded global optimization, global mixedinteger nonlinear programming, and exponential sum model tting. The GUI also runs the linear programming problems in the linear and discrete optimization toolbox OPERA TB. Both NLPLIB TB and OPERA TB are part of TOMLAB � an environment in Matlab for research and teaching in optimization. Presently, NLPLIB TB implements more than 25 solver algorithms, and it is possible to call solvers in the Math Works Optimization Toolbox. MEX le interfaces are developed for seven Fortran and C solvers, and others are easily added using the same type of interface routines. There are four ways to solve a problem: by a direct call to the solver routine or a call to amultisolver driver routine, or interactively, using the Graphical User Interface or a menu system. The GUI may alsobe used as a preprocessor to generate Matlab code for standalone runs. Alargeset of standard test problems is implemented in TOMLAB. Furthermore, using MEX le interfaces, problems in the CUTE test problem data base and problems de ned in the AMPL modeling language can be solved.
Computational Fluid Dynamics for Aerodynamic Design: Its . . .
 Its Current and Future Impact, AIAA 20010538, 39th AIAA Aerospace Sciences Meeting & Exhibit
, 2001
"... This paper discusses the role that computational fluid dynamics plays in the design of aircraft. An overview of the design process is provided, covering some of the typical decisions that a design team addresses within a multidisciplinary environment. On a very regular basis tradeoffs between disc ..."
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Cited by 13 (7 self)
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This paper discusses the role that computational fluid dynamics plays in the design of aircraft. An overview of the design process is provided, covering some of the typical decisions that a design team addresses within a multidisciplinary environment. On a very regular basis tradeoffs between disciplines have to be made where a set of conflicting requirements exist. Within an aircraft development project, we focus on the aerodynamic design problem and review how this process has been advanced, first with the improving capabilities of traditional computational fluid dynamics analyses, and then with aerodynamic optimizations based on these increasingly accurate methods. The optimization method of the present work is based on the use of the adjoint of the flow equations to compute the gradient of the cost function. Then, we use this gradient to navigate the design space in an efficient manner to find a local minimum. The computational costs of the present method are compared with that of other approaches to aerodynamic optimization. A brief discussion regarding the formulation of a continuous adjoint, as opposed to a discrete one, is also included. Two case studies are provided...