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User’s Guide For QPOPT 1.0: A Fortran Package For Quadratic Programming
, 1995
"... QPOPT is a set of Fortran subroutines for minimizing a general quadratic function subject to linear constraints and simple upper and lower bounds. QPOPT may also be used for linear programming and for finding a feasible point for a set of linear equalities and inequalities. If the quadratic function ..."
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Cited by 25 (3 self)
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QPOPT is a set of Fortran subroutines for minimizing a general quadratic function subject to linear constraints and simple upper and lower bounds. QPOPT may also be used for linear programming and for finding a feasible point for a set of linear equalities and inequalities. If the quadratic function is convex (i.e., the Hessian is positive definite or positive semidefinite), the solution obtained will be a global minimizer. If the quadratic is nonconvex (i.e., the Hessian is indefinite), the solution obtained will be a local minimizer or a deadpoint. A twophase activeset method is used. The first phase minimizes the sum of infeasibilities. The second phase minimizes the quadratic function within the feasible region, using a reduced Hessian to obtain search directions. The method is most efficient when many constraints or bounds are active at the solution. QPOPT is not intended for large sparse problems, but there is no fixed limit on problem size. The source code is suitable for all scientific machines with a Fortran 77
An Efficient Multiblock Method for Aerodynamic Analysis and Design on Distributed Memory Systems
, 1997
"... The work presented in this paper describes the application of a multiblock gridding strategy to the solution of aerodynamic design optimization problems involving complex configurations. The design process is parallelized using the MPI (Message Passing Interface) Standard such that it can be efficie ..."
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Cited by 22 (16 self)
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The work presented in this paper describes the application of a multiblock gridding strategy to the solution of aerodynamic design optimization problems involving complex configurations. The design process is parallelized using the MPI (Message Passing Interface) Standard such that it can be efficiently run on a variety of distributed memory systems ranging from traditional parallel computers to networks of workstations. Substantial improvements to the parallel performance of the baseline method are presented, with particular attention to their impact on the scalability of the program as a function of the mesh size. Drag minimization calculations at a fixed coefficient of lift are presented for a business jet configuration that includes the wing, body, pylon, aftmounted nacelle, and vertical and horizontal tails. An aerodynamic design optimization is performed with both the Euler and Reynolds Averaged NavierStokes (RANS) equations governing the flow solution and the results are compared. These sample calculations establish the feasibility of efficient aerodynamic optimization of complete aircraft configurations using the RANS equations as the flow model. There still exists, however, the need for detailed studies of the importance of a true viscous adjoint method which holds the promise of tackling the minimization of not only the wave and induced components of drag, but also the viscous drag.
Exponential Families
, 1990
"... General methods for obtaining maximum likelihood estimates in exponential families are demonstrated using a constrained autologistic model for estimating relatedness from DNA fingerprint data. The novel features are the use of constrained optimization and two new algorithms for maximum likelihood es ..."
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Cited by 20 (4 self)
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General methods for obtaining maximum likelihood estimates in exponential families are demonstrated using a constrained autologistic model for estimating relatedness from DNA fingerprint data. The novel features are the use of constrained optimization and two new algorithms for maximum likelihood estimation. The first, the "phase I " algorithm determines the support of the MLE in the closure of the exponential family (a distribution in the family conditioned on a face of the convex support of the natural statistic) when the MLE does not exist in the traditional sense (a point in the natural parameter space). The second, the maximum Monte Carlo likelihood algorithm uses the Metropolis algorithm or the Gibbs sampler to obtain estimates when exact calculation of the likelihood is not possible. Separate papers on each algorithm accompany
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.
Geometric modelling of the human torso using cubic Hermite elements
, 1995
"... We discuss the advantages and problems associated with fitting geometric data of the human torso obtained from magnetic resonance imaging, with high order (bicubic Hermite) surface elements. These elements preserve derivative (C 1 ) continuity across element boundaries and permit smooth anatomical ..."
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Cited by 19 (5 self)
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We discuss the advantages and problems associated with fitting geometric data of the human torso obtained from magnetic resonance imaging, with high order (bicubic Hermite) surface elements. These elements preserve derivative (C 1 ) continuity across element boundaries and permit smooth anatomically accurate surfaces to be obtained with relatively few elements. These elements are fitted to the data with a new nonlinear fitting procedure that minimises the error in the fit whilst maintaining C 1 continuity with nonlinear constraints. Nonlinear Sobelov smoothing is also incorporated into this fitting scheme. The structures fitted along with their corresponding Root Mean Squared (RMS) error, number of elements used and number of degreesoffreedom (dof) per variable are: epicardium (0.91 mm, 40 elements, 142 dof), left lung (1.66 mm, 80 elements, 309 dof), right lung (1.69 mm, 80 elements, 309 dof), skeletal muscle surface (1.67 mm, 264 elements, 1010 dof), fat layer (1.79 mm, 264 e...
An SQP method for the optimal control of largescale dynamical systems
, 2000
"... We propose a sequential quadratic programming (SQP) method for the optimal control of largescale dynamical systems. The method uses modified multiple shooting to discretize the dynamical constraints. When these systems have relatively few parameters, the computational complexity of the modified met ..."
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Cited by 18 (4 self)
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We propose a sequential quadratic programming (SQP) method for the optimal control of largescale dynamical systems. The method uses modified multiple shooting to discretize the dynamical constraints. When these systems have relatively few parameters, the computational complexity of the modified method is much less than that of standard multiple shooting. Moreover, the proposed method is demonstrably more robust than single shooting. In the context of the SQP method, the use of modified multiple shooting involves a transformation of the constraint Jacobian. The affected rows are those associated with the continuity constraints and any path constraints applied within the shooting intervals. Path constraints enforced at the shooting points (and other constraints involving only discretized states) are not transformed. The transformation is cast almost entirely at the user level and requires minimal changes to the optimization software. We show that the modified quadratic subproblem yields a descent direction for the l_1 penalty function. Numerical experiments verify the efficiency of the modified method.
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 17 (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...
A Set Oriented Approach To Global Optimal Control
 ESAIM: CONTROL, OPTIMISATION AND CALCULUS OF VARIATIONS
, 1999
"... We describe an algorithm for computing the value function for "all source, single destination " discretetime nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discreti ..."
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Cited by 15 (6 self)
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We describe an algorithm for computing the value function for "all source, single destination " discretetime nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graphtheoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path problem on a finite graph. The method is illustrated by two numerical examples, namely a single pendulum on a cart and a parametrically driven inverted double pendulum.
Formulations for SurrogateBased Optimization with DataFit, Multifidelity and ReducedOrder Models
 Proceedings of the 11 th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, No. 20067117 in AIAA Paper
, 2006
"... Surrogatebased optimization (SBO) methods have become established as effective techniques for engineering design problems through their ability to tame nonsmoothness and reduce computational expense. Possible surrogate modeling techniques include data fits (local, multipoint, or global), multifidel ..."
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Cited by 15 (1 self)
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Surrogatebased optimization (SBO) methods have become established as effective techniques for engineering design problems through their ability to tame nonsmoothness and reduce computational expense. Possible surrogate modeling techniques include data fits (local, multipoint, or global), multifidelity model hierarchies, and reducedorder models, and each of these types has unique features when employed within SBO. This paper explores a number of SBO algorithmic variations and their effect for different surrogate modeling cases. First, general facilities for constraint management are explored through approximate subproblem formulations (e.g., direct surrogate), constraint relaxation techniques (e.g., homotopy), merit function selections (e.g., augmented Lagrangian), and iterate acceptance logic selections (e.g., filter methods). Second, techniques specialized to particular surrogate types are described. Computational results are presented for sets of algebraic test problems and an engineering design application solved using the DAKOTA software. I.
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 14 (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.