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On the attraction of Newton’s method to critical lagrange multipliers
Computational Mathematics and Mathematical Physics, 2013Summary: The attraction of dual trajectories of Newton's method for the Lagrange system to critical-Lagrange multipliers is analyzed. This stable effect, which has been confirmed by numerical practice,-leads to the Newton-Lagrange method losing its superlinear convergence when applied to problems with-irregular constraints.
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Overlapping Domain Decomposition methods with distributed Lagrange multipliers
Journal of Numerical Mathematics, 2001An overlapping domain decomposition method for second-order elliptic boundary-value problems is studied. Nonmatching simplicial triangulations are employed for the subdomains while the coupling conditions are enforced by means of distributed Lagrange multipliers. The LBB condition is verified and an efficient preconditioner is suggested.
Hoppe, Ronald H. W., Kuznetsov, Yuri A.
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The Method of Lagrange Multipliers for the Class of Subsmooth Mappings
Mathematical Notes, 2018The author extends the classical Lagrange method to the wide class of so-called subsmooth mappings in Banach spaces; these mappings are related to the notion of strong compact subdifferential introduced recently in his paper. He also relies on his paper [ibid. 99, No. 4, 619--622 (2016; Zbl 1362.47052); translation from Mat. Zametki 99, No. 4, 631--634
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Constrained Minimization Problems (Method of Lagrange Multipliers)
1992We consider the following type of minimization problem. Given a real valued function f on an open nonempty subset U of a real Banach space E we are looking for a minimum of f on the subset of U which is determined by the constraint condition \(g(x)=y\) where \(g: U \longrightarrow F\) is a given function on U with values in some Banach space F and \(y ...
Philippe Blanchard, Erwin Brüning
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On the connection between the stabilized Lagrange multiplier and Nitsche’s methods
Numerische Mathematik, 2015This paper deals with a domain decomposition for the Poisson problem, where the domain are meshed independently and then joined together weakly using either the stabilized Lagrange multiplier or Nitsche's method. The connection between the methods is used to derive robust Nitsche's method. Stability and a priori analysis in the mean dependent norms are
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One Feature of Using the General Lagrange Multiplier Method
Computational Mathematics and Mathematical Physics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Albu, A. F., Zubov, V. I.
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A Generalized Lagrange-Multiplier Method for Constrained Matrix Games
Operations Research, 1971This paper presents a general method for solving constrained matrix games of a type occurring frequently in military and industrial operations research. The usual context is the optimal allocation of constrained resources by two opposing sides among a series of independent cells such that the payoff overall is the sum of the payoffs at each cell.
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A quick derivation of the Lagrange multiplier method
International Journal of Mathematical Education in Science and Technology, 1981A short, direct derivation of the Lagrange multiplier method which avoids complicated interpretations is presented.
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Initial Lagrange Multipliers for the Shooting Method
Journal of Guidance, Control, and Dynamics, 2008T HE purpose of this Note is to concisely discuss the analytical aspects of a number of methods for obtaining initial Lagrange multipliers for the shooting method. Because the ultimate goal is to use the shooting method, the partial derivatives of the state equation with respect to the time, the state, and the control are available and can be used to ...
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