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16
On the limited memory BFGS method for large scale optimization
 Mathematical Programming
, 1989
"... this paper has appeared in ..."
Using ADIFOR to Compute Dense and Sparse Jacobians
 TECHNICAL MEMORANDUM. ANL/MCSTM158, MATHEMATICS AND COMPUTER SCIENCE DIVISION, ARGONNE NATIONAL LABORATORY
, 1992
"... ADIFOR is a source translator that, given a collection of Fortran subroutines for the computation of a "function," produces Fortran code for the computation of the derivatives of this function. More specifically, ADIFOR produces code to compute the matrixmatrix product JS, where J is the Jacobian o ..."
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Cited by 19 (18 self)
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ADIFOR is a source translator that, given a collection of Fortran subroutines for the computation of a "function," produces Fortran code for the computation of the derivatives of this function. More specifically, ADIFOR produces code to compute the matrixmatrix product JS, where J is the Jacobian of the "function" with respect to the userdefined independent variables, and S is the composition of the derivative objects corresponding to the independent variables. This interface is flexible; by setting S = x, one can compute the matrixvector product Jx, or by setting S = I, one can compute the whole Jacobian J . Other initializations of S allow one to exploit a known sparsity structure of J. This paper illustrates the proper initialization of ADIFORgenerated derivative codes and the exploitation of a known sparsity structure of J.
Efficient numerical methods for nonlinear mpc and moving horizon estimation. Nonlinear Model Predictive Control
, 2009
"... exploitation This overview paper reviews numerical methods for solution of optimal control problems in realtime, as they arise in nonlinear model predictive control (NMPC) as well as in moving horizon estimation (MHE). In the first part, we review numerical optimal control solution methods, focussi ..."
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Cited by 18 (0 self)
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exploitation This overview paper reviews numerical methods for solution of optimal control problems in realtime, as they arise in nonlinear model predictive control (NMPC) as well as in moving horizon estimation (MHE). In the first part, we review numerical optimal control solution methods, focussing exclusively on a discrete time setting. We discuss several algorithmic ”building blocks ” that can be combined to a multitude of algorithms. We start by discussing the sequential and simultaneous approaches, the first leading to smaller, the second to more structured optimization problems. The two big families of Newton type optimization methods, Sequential Quadratic Programming (SQP) and Interior Point (IP) methods, are presented, and we discuss how to exploit the optimal control structure in the solution of the linearquadratic subproblems, where the two major alternatives are “condensing ” and band structure exploiting approaches. The second part of the paper discusses how the algorithms can be adapted to the realtime challenge of NMPC and MHE. We recall an important sensitivity result from parametric optimization, and show that a tangential solution predictor for online data can easily be generated in Newton type algorithms. We point out one important difference between SQP and IP methods: while both methods are able to generate the tangential predictor for fixed active sets, the SQP predictor even works across active set changes. We then classify many proposed realtime optimization approaches from the literature into the developed categories. 1
ADIFOR 2.0 user's guide (Revision D)
 TECHNICAL MEMORANDUM ANL/MCSTM192, MATHEMATICS AND COMPUTER SCIENCE DIVISION, ARGONNE NATIONAL LABORATORY
, 1998
"... ..."
An overview of unconstrained optimization
 Online]. Available: citeseer.ist.psu.edu/fletcher93overview.html 150
, 1993
"... bundle filter method for nonsmooth nonlinear ..."
BFGS with update skipping and varying memory
 SIAM J. Optim
, 1998
"... Abstract. We give conditions under which limitedmemory quasiNewton methods with exact line searches will terminate in n steps when minimizing ndimensional quadratic functions. We show that although all Broyden family methods terminate in n steps in their fullmemory versions, only BFGS does so wi ..."
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Cited by 11 (2 self)
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Abstract. We give conditions under which limitedmemory quasiNewton methods with exact line searches will terminate in n steps when minimizing ndimensional quadratic functions. We show that although all Broyden family methods terminate in n steps in their fullmemory versions, only BFGS does so with limitedmemory. Additionally, we show that fullmemory Broyden family methods with exact line searches terminate in at most n + p steps when p matrix updates are skipped. We introduce new limitedmemory BFGS variants and test them on nonquadratic minimization problems.
Benchmark functions for the cec’2010 special session and competition on largescale global optimization
 Nature Inspired Computation and Applications Laboratory
, 2009
"... In the past decades, different kinds of metaheuristic optimization algorithms [1, 2] have been developed; Simulated ..."
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Cited by 7 (6 self)
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In the past decades, different kinds of metaheuristic optimization algorithms [1, 2] have been developed; Simulated
Analyse und Restrukturierung eines Verfahrens zur direkten Lösung von OptimalSteuerungsproblemen (The Theory of MUSCOD in a Nutshell)
, 1995
"... MUSCOD (MU ltiple Shooting COde for Direct Optimal Control) is the implementation of an algorithm for the direct solution of optimal control problems. The method is based on multiple shooting combined with a sequential quadratic programming (SQP) technique; its original version was developed in the ..."
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Cited by 4 (0 self)
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MUSCOD (MU ltiple Shooting COde for Direct Optimal Control) is the implementation of an algorithm for the direct solution of optimal control problems. The method is based on multiple shooting combined with a sequential quadratic programming (SQP) technique; its original version was developed in the early 1980s by Plitt under the supervision of Bock [Plitt81, Bock84]. The following report is intended to describe the basic aspects of the underlying theory in a concise but readable form. Such a description is not yet available: the paper by Bock and Plitt [Bock84] gives a good overview of the method, but it leaves out too many important details to be a complete reference, while the diploma thesis by Plitt [Plitt81], on the other hand, presents a fairly complete description, but is rather difficult to read. Throughout the present document, emphasis is given to a clear presentation of the concepts upon which MUSCOD is based. An effort has been made to properly reflect the structure of the a...
A Boundary Value Problem Approach to the Optimization of Chemical Processes Described by DAE Models
, 1997
"... An efficient and robust technique for the optimization of dynamic chemical processes is presented. In particular, we address the solution of large, multistage optimal control and design optimization problems for processes described by DAE models of index one. Our boundary value problem approach (a ..."
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Cited by 4 (0 self)
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An efficient and robust technique for the optimization of dynamic chemical processes is presented. In particular, we address the solution of large, multistage optimal control and design optimization problems for processes described by DAE models of index one. Our boundary value problem approach (a simultaneous solution strategy) is based on a piecewise parametrization of the control functions and a multiple shooting discretization of the DAEs, combined with a specifically tailored SQP technique. The inherent problem structure is exploited on various levels in order to obtain an efficient overall method. In addition, the formulation lends itself well to parallel computation. Unlike other simultaneous strategies based on collocation, direct use is made of existing advanced, fully adaptive DAE solvers. An implementation of this strategy is provided by the recently developed modular optimal control package MUSCODII. Apart from a difficult DAE test problem with control and path constrain...
ModelBased Partitioning in Optimal Design of Large Engineering Systems
"... The article describes a method to identify weaklyconnected structures in design optimization modelsan optimization problem in itself. A model is represen ted by ahypergraph in which nodes represent design relations (i.e., design objectives and constraints) and hyperedges represent design and ..."
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Cited by 3 (3 self)
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The article describes a method to identify weaklyconnected structures in design optimization modelsan optimization problem in itself. A model is represen ted by ahypergraph in which nodes represent design relations (i.e., design objectives and constraints) and hyperedges represent design and state/behavior variables. Optimal modelbased partitioning of the problem is then solv ed using graph and hypergraph partitioning techniques, such as spectral and local search methods. The formulation is able to account for computational demands and resources, strength of coupling between design relations, and partitioning constraints of decompositionbycomponents and decompositionbydisciplines. Automotive powertrain system and structural optimization models are used as examples. The method may also be used to organize the design process.