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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...
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 11 (2 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.
The TOMLAB OPERA Toolbox for Linear and Discrete Optimization. Advanced Modeling and Optimization
, 1999
"... The Matlab toolbox OPERA TB is a set of Matlab m les, which solves basic linear and discrete optimization problems in operations research and mathematical programming. Included are routines for linear programming (LP), network programming (NP), integer programming (IP) and dynamic programming (DP). ..."
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Cited by 9 (8 self)
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The Matlab toolbox OPERA TB is a set of Matlab m les, which solves basic linear and discrete optimization problems in operations research and mathematical programming. Included are routines for linear programming (LP), network programming (NP), integer programming (IP) and dynamic programming (DP). OPERA TB, like the nonlinear programming toolbox NLPLIB TB, is a part of TOMLAB � an environment in Matlab for research and teaching in optimization. Linear programs are solved either by direct call to a solver routine or to a multisolver driver routine, or interactively, using the Graphical User Interface (GUI) or a menu system. From OPERA TB it is possible to call solvers in the Math Works Optimization Toolbox and, using a MEX le interface, generalpurpose solvers implemented in Fortran or C. The focus is on dense problems, but sparse linear programs may be solved using the commercial solver MINOS. Presently, OPERA TB implements about thirty algorithms and includes a set of test examples and demonstration les. This paper gives an overview of OPERA TB and presents test results for medium size LP problems. The tests show that the OPERA TB solver converges as fast as commercial Fortran solvers and is at least ve times faster than the simplex LP solver in the Optimization Toolbox 2.0andtwice as fast as the primaldual interiorpointLP solver in the same toolbox. Running the commercial Fortran solvers using MEX le interfaces gives a speedup factor of ve to thirty ve.
The TOMLAB NLPLIB Toolbox for Nonlinear Programming. Advanced Modeling and Optimization
, 1999
"... The paper presents the toolbox NLPLIB TB 1.0 (NonLinear Programming LIBrary) � 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 globa ..."
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Cited by 9 (7 self)
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The paper presents the toolbox NLPLIB TB 1.0 (NonLinear Programming LIBrary) � 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. NLPLIB TB, like the toolbox OPERA TB for linear and discrete optimization, is a part of TOMLAB � an environment in Matlab for research and teaching in optimization. TOMLAB currently solves small and medium size dense problems. Presently, NLPLIB TB implements more than 25 solver algorithms, and it is possible to call solvers in the Matlab Optimization Toolbox. MEX le interfaces are prepared for seven Fortran and C solvers, and others are easily added using the same type of interface routines. Currently, MEX le interfaces have beendeveloped for MINOS, NPSOL, NPOPT, NLSSOL, LPOPT, QPOPT and LSSOL. 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
LargeScale Nonlinear Constrained Optimization: A Current Survey
, 1994
"... . Much progress has been made in constrained nonlinear optimization in the past ten years, but most largescale problems still represent a considerable obstacle. In this survey paper we will attempt to give an overview of the current approaches, including interior and exterior methods and algorithm ..."
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Cited by 9 (0 self)
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. Much progress has been made in constrained nonlinear optimization in the past ten years, but most largescale problems still represent a considerable obstacle. In this survey paper we will attempt to give an overview of the current approaches, including interior and exterior methods and algorithms based upon trust regions and line searches. In addition, the importance of software, numerical linear algebra and testing will be addressed. We will try to explain why the difficulties arise, how attempts are being made to overcome them and some of the problems that still remain. Although there will be some emphasis on the LANCELOT and CUTE projects, the intention is to give a broad picture of the stateoftheart. 1 IBM T.J. Watson Research Center, P.O.Box 218, Yorktown Heights, NY 10598, USA 2 Parallel Algorithms Team, CERFACS, 42 Ave. G. Coriolis, 31057 Toulouse Cedex, France 3 Central Computing Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England ...
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 9 (3 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...
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 discretization of ..."
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Cited by 8 (4 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.
On Kolmogorov's Representation of Functions of Several Variables by Functions of One Variable
, 2003
"... This paper proposes a nonparametric estimator for general regression functions with multiple regressors. The method used here is motivated by a remarkable result derived by Kolmogorov (1957) and later tightened by Lorentz (1966). In short, any continuous function f(x 1 ; : : : ; x d ) has the repres ..."
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Cited by 8 (3 self)
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This paper proposes a nonparametric estimator for general regression functions with multiple regressors. The method used here is motivated by a remarkable result derived by Kolmogorov (1957) and later tightened by Lorentz (1966). In short, any continuous function f(x 1 ; : : : ; x d ) has the representation P 2d+1 k=1 ~ g( 1 ~ OE k (x 1 ) + \Delta \Delta \Delta + d ~ OE k (x d )), where ~ g(\Delta) is a continuous function, OE k (\Delta), k = 1; : : : ; 2d + 1, is Lipschitz of order one and strictly increasing, and j , j = 1; : : : ; d, is some constant. Extending this result to the case of smoother functions, we restrict f(\Delta) to be of the form k=1 g k ( k;1 OE k (x 1 ) + \Delta \Delta \Delta + k;d OE k (x d )), 1 t ! 1, where both g k (\Delta) and OE k (\Delta) are three times continuously differentiable and OE k (\Delta) is nondecreasing. These functions are estimated using regression cubic Bsplines, which have excellent numerical and approximating properties. One of the main contributions of this paper is that we develop a method for imposing monotonicity on the cubic Bsplines, a priori, such that the estimator is dense in the set of all monotonic cubic Bsplines. The method requires only 2(r+1)+1 restrictions per each OE k (\Delta), where r is the number of interior knots. Rates of convergence in L 2 are the same as the optimal rate for the onedimensional case. A simulation experiment shows that the estimator works well when t is small, f(\Delta) does not belong to this class of linear superpositions, and optimization is performed using the backfitting algorithm. The monotonic restriction has many other applications besides the one presented here, such as estimating a demand function. With only r + 2 more constraints, it is also possible to impose ...
Transformations To Additivity In Measurement Error Models
, 1996
"... this article, we consider the set of functions G such that G(X; U) = H ..."
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Cited by 6 (1 self)
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this article, we consider the set of functions G such that G(X; U) = H
Designing Environmentally Safe Refrigerants Using Mathematical Programming
 Mathematical Programming. Chemical Engineering Science
, 1996
"... Computer aided molecular design is a strategy in which a set of structural groups are systematically combined to form molecules with desired properties. In this paper, a mathematical programming based approach to computer aided molecular design is presented. Using a set of structural groups, the pro ..."
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Cited by 6 (4 self)
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Computer aided molecular design is a strategy in which a set of structural groups are systematically combined to form molecules with desired properties. In this paper, a mathematical programming based approach to computer aided molecular design is presented. Using a set of structural groups, the problem is formulated as a mixed integer nonlinear program in which discrete variables represent the number of each type of structural groups present in the candidate compound. The augmentedpenalty /outerapproximation algorithm is used to solve the MINLP to obtain compound(s) with an optimum value of an appropriate performance index such that molecular structural constraints, physical property constraints and process design limitations are met. With the current renewed interest in the environment, the suggested approach is applied to refrigerant design with an environmental constraint. The results indicate the viability of this approach. INTRODUCTION The chemical industry is constantly explo...