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24
On the convergence of reflective Newton methods for largescale nonlinear minimization subject to bounds
, 1992
"... . We consider a new algorithm, a reflective Newton method, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach generates strictly feasible iterates by following piecewise linear paths ("reflection" ..."
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Cited by 60 (4 self)
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. We consider a new algorithm, a reflective Newton method, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach generates strictly feasible iterates by following piecewise linear paths ("reflection" paths) to generate improved iterates. The reflective Newton approach does not require identification of an "activity set". In this report we establish that the reflective Newton approach is globally and quadratically convergent. Moreover, we develop a specific example of this general reflective path approach suitable for largescale and sparse problems. 1 Research partially supported by the Applied Mathematical Sciences Research Program (KC04 02) of the Office of Energy Research of the U.S. Department of Energy under grant DEFG0286ER25013. A000, and in part by NSF, AFOSR, and ONR through grant DMS8920550, and by the Cornell Theory Center which receives major funding from the National Sci...
A New Trust Region Algorithm For Equality Constrained Optimization
, 1995
"... . We present a new trust region algorithm for solving nonlinear equality constrained optimization problems. At each iterate a change of variables is performed to improve the ability of the algorithm to follow the constraint level sets. The algorithm employs L 2 penalty functions for obtaining global ..."
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Cited by 51 (7 self)
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. We present a new trust region algorithm for solving nonlinear equality constrained optimization problems. At each iterate a change of variables is performed to improve the ability of the algorithm to follow the constraint level sets. The algorithm employs L 2 penalty functions for obtaining global convergence. Under certain assumptions we prove that this algorithm globally converges to a point satisfying the second order necessary optimality conditions; the local convergence rate is quadratic. Results of preliminary numerical experiments are presented. 1. Introduction. We consider the equality constrained optimization problem minimize f(x) subject to c(x) = 0 (1:1) where x 2 ! n and f : ! n ! !, and c : ! n ! ! m are smooth nonlinear functions. Problem (1.1) is often solved by successive quadratic programming (SQP) methods. At a current point x k 2 ! n , SQP methods determine a search direction d k by solving a quadratic programming problem minimize rf(x k ) T d + 1 2 ...
Image Mosaicing and Superresolution
, 2004
"... The thesis investigates the problem of how information contained in multiple, overlapping images of the same scene may be combined to produce images of superior quality. This area, generically titled frame fusion, offers the possibility of reducing noise, extending the field of view, removal of movi ..."
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Cited by 50 (4 self)
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The thesis investigates the problem of how information contained in multiple, overlapping images of the same scene may be combined to produce images of superior quality. This area, generically titled frame fusion, offers the possibility of reducing noise, extending the field of view, removal of moving objects, removing blur, increasing spatial resolution and improving dynamic range. As such, this research has many applications in fields as diverse as forensic image restoration, computer generated special effects, video image compression, and digital video editing. An essential enabling step prior to performing frame fusion is image registration, by which an accurate estimate of the pointtopoint mapping between views is computed. A robust and efficient algorithm is described to automatically register multiple images using only information contained within the images themselves. The accuracy of this method, and the statistical assumptions upon which it relies, are investigated empirically. Two forms of framefusion are investigated. The first is image mosaicing, which is the alignment of multiple images into a single composition representing part of a 3D scene.
A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables
, 1992
"... . We propose a new algorithm, a reflective Newton method, for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables. The method applies to a general (indefinite) quadratic function, for which a local minimizer subject to bounds is requi ..."
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Cited by 49 (1 self)
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. We propose a new algorithm, a reflective Newton method, for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables. The method applies to a general (indefinite) quadratic function, for which a local minimizer subject to bounds is required, and is particularily suitable for the largescale problem. Our new method exhibits strong convergence properties, global and quadratic convergence, and appears to have significant practical potential. Strictly feasible points are generated. Experimental results on moderately large and sparse problems support the claim of practicality for largescale problems. 1 Research partially supported by the Applied Mathematical Sciences Research Program (KC04 02) of the Office of Energy Research of the U.S. Department of Energy under grant DEFG0286ER25013. A000, and by the Computational Mathematics Program of the National Science Foundation under grant DMS8706133, and by the Cornell Theory Cen...
A Subspace, Interior, and Conjugate Gradient Method for LargeScale BoundConstrained Minimization Problems
 SIAM Journal on Scientific Computing
, 1999
"... A subspace adaptation of the ColemanLi trust region and interior method is proposed for solving largescale boundconstrained minimization problems. This method can be implemented with either sparse Cholesky factorization or conjugate gradient computation. Under reasonable conditions the convergenc ..."
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Cited by 35 (1 self)
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A subspace adaptation of the ColemanLi trust region and interior method is proposed for solving largescale boundconstrained minimization problems. This method can be implemented with either sparse Cholesky factorization or conjugate gradient computation. Under reasonable conditions the convergence properties of this subspace trust region method are as strong as those of its fullspace version.
TwoStep Algorithms for Nonlinear Optimization with Structured Applications
 SIAM Journal on Optimization
, 1999
"... In this paper we propose extensions to trustregion algorithms in which the classical step is augmented with a second step that we insist yields a decrease in the value of the objective function. The classical convergence theory for trustregion algorithms is adapted to this class of twostep alg ..."
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Cited by 10 (6 self)
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In this paper we propose extensions to trustregion algorithms in which the classical step is augmented with a second step that we insist yields a decrease in the value of the objective function. The classical convergence theory for trustregion algorithms is adapted to this class of twostep algorithms. The algorithms can be applied to any problem with variable(s) whose contribution to the objective function is a known functional form. In the nonlinear programming package LANCELOT, they have been applied to update slack variables and variables introduced to solve minimax problems, leading to enhanced optimization eciency. Extensive numerical results are presented to show the eectiveness of these techniques. Keywords. Trust regions, line searches, twostep algorithms, spacer steps, slack variables, LANCELOT, minimax problems, expensive function evaluations, circuit optimization. AMS subject classications. 49M37, 90C06, 90C30 1 Introduction In nonlinear optimization proble...
A Review of Trust Region Algorithms for Optimization
"... Iterative methods for optimization can be classified into two categories: line search methods and trust region methods. In this paper we give a review on trust region algorithms for nonlinear optimization. Trust region methods are robust, and can be applied to illconditioned problems. A model trust ..."
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Cited by 4 (0 self)
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Iterative methods for optimization can be classified into two categories: line search methods and trust region methods. In this paper we give a review on trust region algorithms for nonlinear optimization. Trust region methods are robust, and can be applied to illconditioned problems. A model trust region algorithm is presented to demonstrate the trust region approaches. Various trust region subproblems and their properties are presented. Convergence properties of trust region algorithms are given. Techniques such as backtracking, nonmonotone and second order correction are also briefly discussed. 1 Introduction Nonlinear optimization problems have the form min x2! n f(x) (1.1) s: t: c i (x) = 0; i = 1; 2; : : : ; m e ; (1.2) c i (x) 0; i = m e + 1; : : : ; m; (1.3) where f(x) and c i (x) (i = 1; : : : ; m) are real functions defined in ! n , at least one of these functions is nonlinear, and m m e are two nonnegative integers. If m = m e = 0, problem (1.1) is an unconstrain...
Dynamic pathway modeling: feasibility analysis and optimal experimental design
 Ann N Y Acad Sci
, 2007
"... ABSTRACT: A major challenge in systems biology is to evaluate the feasibility of a biological research project prior to its realization. Since experiments are animals, cost and timeconsuming, approaches allowing researchers to discriminate alternative hypotheses with a minimal set of experiments ..."
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Cited by 3 (2 self)
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ABSTRACT: A major challenge in systems biology is to evaluate the feasibility of a biological research project prior to its realization. Since experiments are animals, cost and timeconsuming, approaches allowing researchers to discriminate alternative hypotheses with a minimal set of experiments are highly desirable. Given a null hypothesis and alternative model, as well as laboratory constraints like observable players, sample size, noise level, and stimulation options, we suggest a method to obtain a list of required experiments in order to significantly reject the null hypothesis model M0 if a specified alternative model MA is realized. For this purpose, we estimate the power to detect a violation of M0 by means of Monte Carlo simulations. Iteratively, the power is maximized over all feasible stimulations of the system using multiexperiment fitting, leading to an optimal combination of experimental settings to discriminate the null hypothesis and alternative model. We prove the importance of simultaneous modeling of combined experiments with quantitative, highly sampled in vivo measurements from the Jak/STAT5 signaling pathway in fibroblasts, stimulated with erythropoietin (Epo). Afterwards we apply the presented iterative experimental design approach to the Jak/STAT3 pathway of primary hepatocytes stimulated with IL6. Our approach offers the possibility of deciding which scientific questions can be answered based on existing laboratory constraints. To be able to concentrate on feasible questions on account of inexpensive computational simulations yields not only enormous cost and time saving, but also helps to specify realizable, systematic research projects in advance.
FlatnessBased EndControl of a Gas Exchange Solenoid Actuator for IC Engines
"... Permission is hereby granted to the University of Alberta to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly, or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis ..."
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Permission is hereby granted to the University of Alberta to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly, or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as hereinbefore provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatever without the author’s prior written permission.