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Snopt: An SQP Algorithm For LargeScale Constrained Optimization
, 1997
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 328 (18 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse.
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 35 (8 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...
Theory and implementation of numerical methods based on RungeKutta integration for solving optimal control problems
, 1996
"... ..."
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 19 (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...
Advances in Simultaneous Strategies for Dynamic Process Optimization
 Optimization, Chemical Engineering Science
, 2001
"... Introduction Over the past decade, applications in dynamic simulation have increased signicantly in the process industries. These are driven by strong competitive markets faced by operating companies along with tighter specications on process performance and regulatory limits. Moreover, the develop ..."
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Cited by 15 (2 self)
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Introduction Over the past decade, applications in dynamic simulation have increased signicantly in the process industries. These are driven by strong competitive markets faced by operating companies along with tighter specications on process performance and regulatory limits. Moreover, the developmentofpowerful commercial modeling tools for dynamic simulation, such as ASPEN Custom # ####### ########################## #### ############### ################### 1 Modeler and gProms, has led to their introduction in industry alongside their widely used steady state counterparts. Dynamic optimization is the natural extension of these dynamic simulation tools because it automates many of the decisions required for engineering studies. Applications of dynamic simulation can be classied into oline and online tasks. Oline tasks include: # Design to avoid undesirable transients for chemical process
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 13 (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)
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 ...
A Reduced Space Interior Point Strategy for Optimization of Differential Algebraic Systems
 Computers & Chemical Engineering
, 1999
"... A novel nonlinear programming (NLP) strategy is developed and applied to the optimization of differential algebraic equation (DAE) systems. Such problems, also referred to as dynamic optimization problems, are common in chemical process engineering and remain challenging applications of nonlinear pr ..."
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Cited by 6 (3 self)
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A novel nonlinear programming (NLP) strategy is developed and applied to the optimization of differential algebraic equation (DAE) systems. Such problems, also referred to as dynamic optimization problems, are common in chemical process engineering and remain challenging applications of nonlinear programming. These applications often consist of large, complex nonlinear models that result from discretizations of DAEs. Variables in the NLP model include state and control variables, with far fewer control variables than states. Moreover, all of these discretized variables have associated upper and lower bounds which can be potentially active. To deal with this large, highly constrained problem, an interior point NLP strategy is developed. Here a log barrier function is used to deal with the large number of bound constraints in order to transform the problem to an equality constrained NLP. A modified Newton method is then applied directly to this problem. In addition, this method uses an efficient decomposition of the discretized DAEs and the solution of the Newton step is performed in the reduced space of the independent variables. The resulting approach exploits many of the features of the DAE system and is performed element by element in a forward manner. Several large dynamic process optimization problems are considered to demonstrate the effectiveness of this approach; these include complex separation and reaction processes (including reactive distillation) with several hundred DAEs. NLP formulations with over 55,000 variables are considered. These problems are solved in 5 to 12 CPU minutes on small workstations. Key words: interior point; dynamic optimization; nonlinear programming 1 1
Optimal Configuration of Spacecraft Formations via a Gauss
 Pseudospectral Method,” AAS Spaceflight Mechanics Meeting, AAS 05103, Copper Mountain
, 2005
"... The problem of determining minimumfuel maneuver sequences for a fourspacecraft formation is considered. The objective of this paper is to determine fueloptimal configuration trajectories that transfer a four spacecraft formation from an initial parking orbit to a desired terminal reference orbit ..."
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Cited by 6 (3 self)
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The problem of determining minimumfuel maneuver sequences for a fourspacecraft formation is considered. The objective of this paper is to determine fueloptimal configuration trajectories that transfer a four spacecraft formation from an initial parking orbit to a desired terminal reference orbit while satisfying particular formation constraints. In this paper, the configuration problem is solved numerically using a newly developed direct transcription method called the Gauss pseudospectral method. Two versions of the minimumfuel configuration problem are considered. In the first problem the trajectory is terminated upon satisfying the required terminal position constraints. In the second problem the trajectory is extended one full orbit beyond that of the first problem such that the terminal conditions are the same as those attained one period earlier. The results obtained in this paper illustrate the key features of the optimal configuration trajectories and controls, provide insight into the structure of the optimally controlled system, and demonstrate the applicability of the Gauss pseudospectral method to optimal formation flying trajectory design. 1
A Sparse Superlinearly Convergent SQP with Applications to Twodimensional Shape Optimization
 Preprint ANL/MCSP7060198, Argonne National Laboratory, Argonne
, 1998
"... Discretization of optimal shape design problems leads to very large nonlinear optimization problems. For attaining maximum computational efficiency, a sequential quadratic programming (SQP) algorithm should achieve superlinear convergence while preserving sparsity and convexity of the resulting quad ..."
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Cited by 5 (0 self)
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Discretization of optimal shape design problems leads to very large nonlinear optimization problems. For attaining maximum computational efficiency, a sequential quadratic programming (SQP) algorithm should achieve superlinear convergence while preserving sparsity and convexity of the resulting quadratic programs. Most classical SQP approaches violate at least one of the requirements. We show that, for a very large class of optimization problems, one can design SQP algorithms that satisfy all these three requirements. The improvements in computational efficiency are demonstrated for a cam design problem. Address all correspondence to this author. y The work of this author was supported by the Mathematical, Information and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W31109Eng38. 1 Introduction Within the class of potentially very large scale problems, shape optimization occupies ...