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Nonlinear Programming without a penalty function
 Mathematical Programming
, 2000
"... In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trustregion algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a "filter" is introduced w ..."
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Cited by 160 (27 self)
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In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trustregion algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a "filter" is introduced which allows a step to be accepted if it reduces either the objective function or the constraint violation function. Numerical tests on a wide range of test problems are very encouraging and the new algorithm compares favourably with LANCELOT and an implementation of Sl 1 QP.
Sequential Quadratic Programming
, 1995
"... this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can ..."
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Cited by 115 (2 self)
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this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can
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 39 (11 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.
Smooth SQP Methods for Mathematical Programs with Nonlinear Complementarity Constraints
 SIAM Journal on Optimization
, 1997
"... Mathematical programs with nonlinear complementarity constraints are reformulated using betterposed but nonsmooth constraints. We introduce a class of functions, parameterized by a real scalar, to approximate these nonsmooth problems by smooth nonlinear programs. This smoothing procedure has the ex ..."
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Cited by 34 (0 self)
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Mathematical programs with nonlinear complementarity constraints are reformulated using betterposed but nonsmooth constraints. We introduce a class of functions, parameterized by a real scalar, to approximate these nonsmooth problems by smooth nonlinear programs. This smoothing procedure has the extra benefits that it often improves the prospect of feasibility and stability of the constraints of the associated nonlinear programs and their quadratic approximations. We present two globally convergent algorithms based on sequential quadratic programming, SQP, as applied in exact penalty methods for nonlinear programs. Global convergence of the implicit smooth SQP method depends on existence of a lowerlevel nondegenerate (strictly complementary) limit point of the iteration sequence. Global convergence of the explicit smooth SQP method depends on a weaker property, i.e. existence of a limit point at which a generalized constraint qualification holds. We also discuss some practical matter...
A reduced Hessian method for largescale constrained optimization
 SIAM JOURNAL ON OPTIMIZATION
, 1995
"... ..."
On Combining Feasibility, Descent and Superlinear Convergence in Inequality Constrained Optimization
 Mathematical Programming
, 1993
"... . Extension of quasiNewton techniques from unconstrained to constrained optimization via Sequential Quadratic Programming (SQP) presents several difficulties. Among these are the possible inconsistency, away from the solution, of first order approximations to the constraints, resulting in infeasibi ..."
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Cited by 29 (1 self)
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. Extension of quasiNewton techniques from unconstrained to constrained optimization via Sequential Quadratic Programming (SQP) presents several difficulties. Among these are the possible inconsistency, away from the solution, of first order approximations to the constraints, resulting in infeasibility of the quadratic programs; and the task of selecting a suitable merit function, to induce global convergence. In the case of inequality constrained optimization, both of these difficulties disappear if the algorithm is forced to generate iterates that all satisfy the constraints, and that yield monotonically decreasing objective function values. (Feasibility of the successive iterates is in fact required in many contexts such as in realtime applications or when the objective function is not well defined outside the feasible set). It has been recently shown that this can be achieved while preserving local twostep superlinear convergence. In this note, the essential ingredients for an S...
Integrating SQP and branchandbound for Mixed Integer Nonlinear Programming
 Computational Optimization and Applications
, 1998
"... This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving ..."
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Cited by 24 (0 self)
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This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems. In contrast, an integrated approach to solving MINLP problems is considered here. This new algorithm is based on branchandbound, but does not require the NLP problem at each node to be solved to optimality. Instead, branching is allowed after each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is solved whilst searching the tree. The nonlinear solver that is considered in this paper is a Sequential Quadratic Programming solver. A numerical comparison of the new method with nonlinear branchandbound is presented and a factor of about 3 improvement over branchandbound is observed...
Dental Biometrics: Alignment and Matching of Dental Radiographs
 IEEE Trans. PAMI
, 2005
"... Dental biometrics utilizes the evidence revealed by dental radiographs for human identification. This evidence includes the tooth contours, the relative positions of neighboring teeth, and the shapes of the dental work (e.g., crowns, fillings and bridges). The proposed system has two main stages: fe ..."
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Cited by 11 (1 self)
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Dental biometrics utilizes the evidence revealed by dental radiographs for human identification. This evidence includes the tooth contours, the relative positions of neighboring teeth, and the shapes of the dental work (e.g., crowns, fillings and bridges). The proposed system has two main stages: feature extraction, and matching. The feature extraction stage uses anisotropic diffusion to enhance the images and a Mixture of Gaussians model to segment the dental work. The matching stage has three sequential steps: shape registration, computation of image similarity, and subject identification. In shape registration, we align the tooth contours and obtain the distance between them. A second method based on overlapped areas is used to match the dental work. The distance between the shapes of the teeth and the distance between the shapes of the dental work are then combined using likelihood estimates to improve the retrieval accuracy. At the second step, the correspondence of teeth between two given images is established. A distance measure based on this correspondence is then used to represent the similarity between the two images. Finally, the distances are used to infer the subject’s identity. 1
Inexact SQP methods for equality constrained optimization
 SIAM J. Opt
"... Abstract. We present an algorithm for largescale equality constrained optimization. The method is based on a characterization of inexact sequential quadratic programming (SQP) steps that can ensure global convergence. Inexact SQP methods are needed for largescale applications for which the iterati ..."
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Cited by 10 (6 self)
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Abstract. We present an algorithm for largescale equality constrained optimization. The method is based on a characterization of inexact sequential quadratic programming (SQP) steps that can ensure global convergence. Inexact SQP methods are needed for largescale applications for which the iteration matrix cannot be explicitly formed or factored and the arising linear systems must be solved using iterative linear algebra techniques. We address how to determine when a given inexact step makes sufficient progress toward a solution of the nonlinear program, as measured by an exact penalty function. The method is globalized by a line search. An analysis of the global convergence properties of the algorithm and numerical results are presented. Key words. largescale optimization, constrained optimization, sequential quadratic programming, inexact linear system solvers, Krylov subspace methods AMS subject classifications. 49M37, 65K05, 90C06, 90C30, 90C55 1. Introduction. In