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115
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... 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 597 (24 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. We discuss
GLOBAL CONVERGENCE PROPERTIES OF CONJUGATE GRADIENT METHODS FOR OPTIMIZATION
, 1992
"... This paper explores the convergence ofnonlinear conjugate gradient methods without restarts, and with practical line searches. The analysis covers two classes ofmethods that are globally convergent on smooth, nonconvex functions. Some properties of the FletcherReeves method play an important role ..."
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Cited by 129 (3 self)
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This paper explores the convergence ofnonlinear conjugate gradient methods without restarts, and with practical line searches. The analysis covers two classes ofmethods that are globally convergent on smooth, nonconvex functions. Some properties of the FletcherReeves method play an important role in the first family, whereas the second family shares an important property with the PolakRibire method. Numerical experiments are presented.
On the resolution of monotone complementarity problems
 Comput. Optim. Appl
, 1996
"... Abstract. A reformulation of the nonlinear complementarity problem (NCP) as an unconstrained minimization problem is considered. It is shown that any stationary point of the unconstrained objective function is already a solution of NCP if the mapping F involved in NCP is continuously differentiable ..."
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Cited by 54 (10 self)
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Abstract. A reformulation of the nonlinear complementarity problem (NCP) as an unconstrained minimization problem is considered. It is shown that any stationary point of the unconstrained objective function is already a solution of NCP if the mapping F involved in NCP is continuously differentiable and monotone. A descent algorithm is described which uses only function values of F. Some numerical results are given.
On the implementation of an algorithm for largescale equality constrained optimization
 SIAM Journal on Optimization
, 1998
"... Abstract. This paper describes a software implementation of Byrd and Omojokun’s trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques ..."
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Cited by 49 (12 self)
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Abstract. This paper describes a software implementation of Byrd and Omojokun’s trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques for solving the subproblems occurring in the algorithm. Second derivative information can be used, but when it is not available, limited memory quasiNewton approximations are made. The performance of the code is studied using a set of difficult test problems from the CUTE collection.
2005), Estimating eddy stresses by fitting dynamics to observations using a residual‐mean ocean circulation model and its adjoint
 J. Phys. Oceanogr
"... A global ocean circulation model is formulated in terms of the “residual mean ” and used to study eddy–mean flow interaction. Adjoint techniques are used to compute the threedimensional eddy stress field that minimizes the departure of the coarseresolution model from climatological observations of ..."
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Cited by 27 (9 self)
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A global ocean circulation model is formulated in terms of the “residual mean ” and used to study eddy–mean flow interaction. Adjoint techniques are used to compute the threedimensional eddy stress field that minimizes the departure of the coarseresolution model from climatological observations of temperature. The resulting 3D maps of eddy stress and residualmean circulation yield a wealth of information about the role of eddies in largescale ocean circulation. In eddyrich regions such as the Southern Ocean, the Kuroshio, and the Gulf Stream, eddy stresses have an amplitude comparable to the wind stress, of order 0.2 N m2, and carry momentum from the surface down to the bottom, where they are balanced by mountain form drag. From the optimized eddy stress, 3D maps of horizontal eddy diffusivity are inferred. The diffusivities have a welldefined largescale structure whose prominent features are 1) large values of (up to 4000 m2 s1) in the western boundary currents and on the equatorial flank of the Antarctic Circumpolar Current and 2) a surface intensification of , suggestive of a dependence on the stratification N 2. It is shown that implementation of an eddy parameterization scheme in which the eddy diffusivity has an N 2 dependence significantly improves the climatology of the ocean model state relative to that obtained using a spatially uniform diffusivity. 1.
A Family of Variable Metric Proximal Methods
, 1993
"... We consider conceptual optimization methods combining two ideas: the MoreauYosida regularization in convex analysis, and quasiNewton approximations of smooth functions. We outline several approaches based on this combination, and establish their global convergence. Then we study theoretically the ..."
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Cited by 26 (2 self)
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We consider conceptual optimization methods combining two ideas: the MoreauYosida regularization in convex analysis, and quasiNewton approximations of smooth functions. We outline several approaches based on this combination, and establish their global convergence. Then we study theoretically the local convergence properties of one of these approaches, which uses quasiNewton updates of the objective function itself. Also, we obtain a globally and superlinearly convergent BFGS proximal method. At each step of our study, we single out the assumptions that are useful to derive the result concerned.
Applications of Multidimensional Scaling to Molecular Conformation
, 1997
"... Multidimensional scaling (MDS) is a collection of data analytic techniques for constructing configurations of points from information about interpoint distances. Such constructions arise in computational chemistry when one endeavors to infer the conformation (3dimensional structure) of a molecule fr ..."
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Cited by 24 (6 self)
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Multidimensional scaling (MDS) is a collection of data analytic techniques for constructing configurations of points from information about interpoint distances. Such constructions arise in computational chemistry when one endeavors to infer the conformation (3dimensional structure) of a molecule from information about its interatomic distances. For a number of reasons, this application of MDS poses computational challenges not encountered in more traditional applications. In this report we sketch the mathematical formulation of MDS for molecular conformation problems and describe two approaches that can be employed for their solution. 1 Molecular Conformation Consider a molecule with n atoms. We can represent its conformation, or 3dimensional structure, by specifying the coordinates of each atom with respect to a Euclidean coordinate system for ! 3 . We store these coordinates in an n \Theta 3 configuration matrix X. Given X, we can easily compute the matrix of interatomic distan...
Assessment of skill and portability in regional marine biogeochemical models: Role of multiple planktonic groups
"... [1] Application of biogeochemical models to the study of marine ecosystems is pervasive, yet objective quantification of these models ’ performance is rare. Here, 12 lower trophic level models of varying complexity are objectively assessed in two distinct regions (equatorial Pacific and Arabian Sea) ..."
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Cited by 24 (4 self)
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[1] Application of biogeochemical models to the study of marine ecosystems is pervasive, yet objective quantification of these models ’ performance is rare. Here, 12 lower trophic level models of varying complexity are objectively assessed in two distinct regions (equatorial Pacific and Arabian Sea). Each model was run within an identical onedimensional physical framework. A consistent variational adjoint implementation assimilating chlorophylla, nitrate, export, and primary productivity was applied and the same metrics were used to assess model skill. Experiments were performed in which data were assimilated from each site individually and from both sites simultaneously. A crossvalidation experiment was also conducted whereby data were assimilated from one site and the resulting optimal parameters were used to generate a simulation for the second site. When a single pelagic regime is considered, the simplest models fit the data as well as those with multiple phytoplankton functional groups. However, those with multiple phytoplankton functional groups produced lower misfits when the models are required to simulate both regimes using identical parameter values. The crossvalidation experiments revealed that as long as only a few key biogeochemical parameters were optimized, the