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SQP Methods And Their Application To Numerical Optimal Control
, 1997
"... . In recent years, generalpurpose sequential quadratic programming (SQP) methods have been developed that can reliably solve constrained optimization problems with many hundreds of variables and constraints. These methods require remarkably few evaluations of the problem functions and can be shown ..."
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Cited by 36 (0 self)
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. In recent years, generalpurpose sequential quadratic programming (SQP) methods have been developed that can reliably solve constrained optimization problems with many hundreds of variables and constraints. These methods require remarkably few evaluations of the problem functions and can be shown to converge to a solution under very mild conditions on the problem. Some practical and theoretical aspects of applying generalpurpose SQP methods to optimal control problems are discussed, including the influence of the problem discretization and the zero/nonzero structure of the problem derivatives. We conclude with some recent approaches that tailor the SQP method to the control problem. Key words. largescale optimization, sequential quadratic programming (SQP) methods, optimal control problems, multiple shooting methods, single shooting methods, collocation methods AMS subject classifications. 49J20, 49J15, 49M37, 49D37, 65F05, 65K05, 90C30 1. Introduction. Recently there has been c...
Design of new daspk for sensitivity analysis
, 1999
"... A new version of DASPK, DASPK3.0, with capability for sensitivity analysis is presented in this report. DASPK3.0 differs from the sensitivity code DASPKSO, described in [12], in several ways. DASPK3.0 has all the features, which were not available in DASPKSO, of the previous version DASPK2.0. One o ..."
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Cited by 28 (10 self)
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A new version of DASPK, DASPK3.0, with capability for sensitivity analysis is presented in this report. DASPK3.0 differs from the sensitivity code DASPKSO, described in [12], in several ways. DASPK3.0 has all the features, which were not available in DASPKSO, of the previous version DASPK2.0. One of these features is an improved algorithm for calculation of consistent initial conditions for indexzero or indexone systems. DASPK3.0 also incorporates a mechanism for initialization and solution of index2 systems. Other improvements in DASPK3.0 include a more accurate error and convergence test, particularly for the sensitivity analysis. We implemented the Krylov method for sensitivity computation with a different strategy from DASPKSO, and made it more efficient and easier for parallel computing. We also added the staggered corrector method [7] for both the direct and Krylov method. We implemented the sensitivity analysis with an internal parallel mode, which is easy to use for both serial and parallel computation with message passing interface (MPI). We also incorporated automatic differentiation into DASPK3.0 to evaluate the Jacobian matrix and sensitivity equations. The goal of our design has been to be compatible as much as possible with DASPK2.0, to minimize memory and storage requirements for sensitivity analysis, and to speed up the computation for a large number of sensitivity parameters.
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.
An Interface Between Optimization and Application for the Numerical Solution of Optimal Control Problems
 ACM Transactions on Mathematical Software
, 1998
"... This paper is concerned with the implementation of optimization algorithms for the solution of smooth discretized optimal control problems. The problems under consideration can be written as min f(y; u) ..."
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Cited by 15 (7 self)
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This paper is concerned with the implementation of optimization algorithms for the solution of smooth discretized optimal control problems. The problems under consideration can be written as min f(y; u)
Halo orbit mission correction maneuvers using optimal control. Automatica 38:571–583
, 2002
"... This paper addresses the computation of the required trajectory correction maneuvers (TCM) for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launch vehicle. By combining dynamical systems theory with optimal control techniques, we are able ..."
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Cited by 15 (5 self)
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This paper addresses the computation of the required trajectory correction maneuvers (TCM) for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launch vehicle. By combining dynamical systems theory with optimal control techniques, we are able to provide a compelling portrait of the complex landscape of the trajectory design space. This approach enables automation of the analysis to perform parametric studies that simply were not available to mission designers a few years ago, such as how the magnitude of the errors and the timing of the first trajectory correction maneuver affects the correction ~ V. The impetus for combining dynamical systems theory and optimal control in this problem arises from design issues for the Genesis Discovery mission being developed for NASA by the Jet Propulsion Laboratory.
Computational Strategies For Shape Optimization Of TimeDependent NavierStokes Flows
, 1997
"... . We consider the problem of shape optimization of twodimensional #ows governed by the timedependentNavierStokes equations. For this problem we propose computational strategies with respect to optimization method, sensitivity method, and unstructured meshing scheme. We argue that, despite their s ..."
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Cited by 7 (0 self)
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. We consider the problem of shape optimization of twodimensional #ows governed by the timedependentNavierStokes equations. For this problem we propose computational strategies with respect to optimization method, sensitivity method, and unstructured meshing scheme. We argue that, despite their superiority for steady NavierStokes #ow optimization, reduced sequential quadratic programming #RSQP# methods are too memoryintensive for the timedependent problem. Instead, we advocate a combination of generalized reduced gradients #for the #ow equation constraints# and SQP #for the remaining inequality constraints#. With respect to sensitivity method, wefavor discrete sensitivities, which can be implemented with little additional storage or work beyond that required for solution of the #ow equations, and thus possess a distinct advantage over discretized continuous sensitivities, which require knowledge of the entire time history of the #ow variables. Finally,we takeatwophase approach t...
Numerical Simulation and Optimal Control of Air Separation Plants
, 1999
"... Numerical simulation has already become an indispensable tool in the chemical engineering industry. In this paper, the extension of an already existing simulation package to the efficient and reliable solution of optimal control problems for optimal plant operation is discussed. ..."
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Cited by 1 (0 self)
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Numerical simulation has already become an indispensable tool in the chemical engineering industry. In this paper, the extension of an already existing simulation package to the efficient and reliable solution of optimal control problems for optimal plant operation is discussed.
Dynamic Optimization Of Chemically Reacting Stagnation Flows
"... This paper presents a dynamicoptimization algorithm that can be used ..."
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This paper presents a dynamicoptimization algorithm that can be used
Large Scale NonLinear Programming for PDE Constrained Optimization.
, 2002
"... Sandia is a multiprogram laboratory operated by Sandia Corporation, ..."