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116
TrustRegion InteriorPoint Algorithms For Minimization Problems With Simple Bounds
 SIAM J. CONTROL AND OPTIMIZATION
, 1995
"... Two trustregion interiorpoint algorithms for the solution of minimization problems with simple bounds are analyzed and tested. The algorithms scale the local model in a way similar to Coleman and Li [1]. The first algorithm is more usual in that the trust region and the local quadratic model are c ..."
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Cited by 56 (18 self)
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Two trustregion interiorpoint algorithms for the solution of minimization problems with simple bounds are analyzed and tested. The algorithms scale the local model in a way similar to Coleman and Li [1]. The first algorithm is more usual in that the trust region and the local quadratic model are consistently scaled. The second algorithm proposed here uses an unscaled trust region. A global convergence result for these algorithms is given and dogleg and conjugategradient algorithms to compute trial steps are introduced. Some numerical examples that show the advantages of the second algorithm are presented.
TrustRegion InteriorPoint SQP Algorithms For A Class Of Nonlinear Programming Problems
 SIAM J. CONTROL OPTIM
, 1997
"... In this paper a family of trustregion interiorpoint SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal co ..."
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Cited by 46 (9 self)
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In this paper a family of trustregion interiorpoint SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal control problems. The algorithms treat states and controls as independent variables. They are designed to take advantage of the structure of the problem. In particular they do not rely on matrix factorizations of the linearized constraints, but use solutions of the linearized state equation and the adjoint equation. They are well suited for large scale problems arising from optimal control problems governed by partial differential equations. The algorithms keep strict feasibility with respect to the bound constraints by using an affine scaling method proposed for a different class of problems by Coleman and Li and they exploit trustregion techniques for equalityconstrained optimizatio...
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 43 (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.
Theory and implementation of numerical methods based on RungeKutta integration for solving optimal control problems
, 1996
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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 35 (5 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...
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 32 (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. ...
A sequential quadratic programming algorithm using an incomplete solution of the subproblem
 SIAM Journal of Optimization
, 1995
"... Ary opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do NOT necessarily reflect the views of the above sponsors. ..."
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Cited by 30 (2 self)
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Ary opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do NOT necessarily reflect the views of the above sponsors.
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 28 (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...
Some theoretical properties of an augmented Lagrangian merit function
 in Advances in Optimization and Parallel Computing
, 1992
"... Sequential quadratic programming (SQP) methods for nonlinearly constrained optimization typically use a merit function to enforce convergence from an arbitrary starting point. We define a smooth augmented Lagrangian merit function in which the Lagrange multiplier estimate is treated as a separate v ..."
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Cited by 27 (6 self)
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Sequential quadratic programming (SQP) methods for nonlinearly constrained optimization typically use a merit function to enforce convergence from an arbitrary starting point. We define a smooth augmented Lagrangian merit function in which the Lagrange multiplier estimate is treated as a separate variable, and inequality constraints are handled by means of nonnegative slack variables that are included in the linesearch. Global convergence is proved for an SQP algorithm that uses this merit function. We also prove that steps of unity are accepted in a neighborhood of the solution when this merit function is used in a suitable superlinearly convergent algorithm. Finally, some numerical results are presented to illustrate the performance of the associated SQP method.
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 27 (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...