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2003
In this chapter we discuss the quasi-Newton versions of the algorithms presented in chapters 12, 13 and 15. Just as in the case of unconstrained problems (see § 4.4), the quasi-Newton approach is useful when one does not want to compute second order derivatives of the functions defining the optimization problem to solve.
J. Frédéric Bonnans +3 more
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In this chapter we discuss the quasi-Newton versions of the algorithms presented in chapters 12, 13 and 15. Just as in the case of unconstrained problems (see § 4.4), the quasi-Newton approach is useful when one does not want to compute second order derivatives of the functions defining the optimization problem to solve.
J. Frédéric Bonnans +3 more
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Quasi-Newton Updates with Bounds
SIAM Journal on Numerical Analysis, 1987In each step of quasi-Newton methods an improved approximate solution \(x_ k\) is determined together with a new approximation \(B_ k\) of the derivative f'. Specifically, Broyden's method yields an update \(B_{k+1}\) which is the solution of the minimum problem: \(\min \{\| B-B_ k\|_ F: Bs_ k=y_ k\}.\) Here \(y_ k\) and \(s_ k\) are vectors which are ...
Calamai, Paul H., Moré, Jorge J.
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Stochastic Quasi-Newton Methods
Proceedings of the IEEE, 2020Large-scale data science trains models for data sets containing massive numbers of samples. Training is often formulated as the solution of empirical risk minimization problems that are optimization programs whose complexity scales with the number of elements in the data set.
Aryan Mokhtari, Alejandro Ribeiro
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Sparse quasi‐Newton LDU updates
International Journal for Numerical Methods in Engineering, 1987AbstractNumerical solution of a given non‐linear algebraic system of equations by a quasi‐Newton type method requires updating the approximation to the Jacobian at each step. Two methods for large sparse systems are described. The approximation for the Jacobian is factored into an LDU form at the first step, then all the subsequent updates are made to ...
Tewarson, R. P., Yin, Zhang
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A Survey of Quasi-Newton Equations and Quasi-Newton Methods for Optimization
Annals of Operations Research, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xu, Chengxian, Zhang, Jianzhong
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2019
The Quasi-Newton methods do not compute the Hessian of nonlinear functions. The Hessian is updated by analyzing successive gradient vectors instead. The Quasi-Newton algorithm was first proposed by William C. Davidon, a physicist while working at Argonne National Laboratory, United States in 1959.
Shashi Kant Mishra, Bhagwat Ram
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The Quasi-Newton methods do not compute the Hessian of nonlinear functions. The Hessian is updated by analyzing successive gradient vectors instead. The Quasi-Newton algorithm was first proposed by William C. Davidon, a physicist while working at Argonne National Laboratory, United States in 1959.
Shashi Kant Mishra, Bhagwat Ram
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Approximate quasi-Newton methods
Mathematical Programming, 1990Newton-like iterative methods for nonlinear equations on Banach spaces are considered. It is proved how the local convergence behaviour of the quasi-Newton method in the infinite dimensional setting is affected by the refinement strategy. Applications to boundary value problems and integral equations are included.
Kelley, C. T., Sachs, E. W.
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Properties and numerical performance of quasi-Newton methods with modified quasi-Newton equations
Journal of Computational and Applied Mathematics, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Jianzhong, Xu, Chengxian
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Full Waveform Inversion Based on Modified Quasi‐Newton Equation Quasi‐Newton Equation
Chinese Journal of Geophysics, 2013AbstractWaveform inversion is a kind of method to reveal the underground structure and lithology through minimizing the residual error between predicted wavefield and true seismic record using full‐wavefield information. In this paper, we briefly present the principle of the conventional Quasi‐Newton algorithm, and then exploit a new modified Quasi ...
LIU Lu +6 more
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1989
In diesem Abschnitt soll ein mathematisch besonders interessanter Weg der Nullstellenbestimmung beschrieben werden. Wir haben bereits in 3.2 gesehen, das die Q-superlinear konvergenten Iterationsverfahren Newton-ahnlich sind. Mit dem gedampften Newtonverfahren haben wir ein global und schnell konvergentes Minimierungsverfahren kennengelernt, bei dem ...
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In diesem Abschnitt soll ein mathematisch besonders interessanter Weg der Nullstellenbestimmung beschrieben werden. Wir haben bereits in 3.2 gesehen, das die Q-superlinear konvergenten Iterationsverfahren Newton-ahnlich sind. Mit dem gedampften Newtonverfahren haben wir ein global und schnell konvergentes Minimierungsverfahren kennengelernt, bei dem ...
openaire +1 more source