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Lagrange Multipliers and Optimality
SIAM Review, 1993Summary: Lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write first-order optimality conditions formally as a system of equations. Modern applications, with their emphasis on numerical methods and more complicated side conditions than equations, have demanded deeper ...
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On a superspray in lagrange superspaces
Reports on Mathematical Physics, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rezaii, M. M., Azizpour, E.
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Publicationes Mathematicae Debrecen, 2022
In this paper, using as model the theory of Lagrange geometry by R. Miron and the total space \(E=\bigoplus^ k_ 1TM\) of a vector bundle, the theory of \(k\)-Lagrange geometry for variational problems of multiple integrals is obtained. Since the metric is derived from a Lagrangian, the theory differs from \textit{Chr. Günther}'s theory [J. Differ. Geom.
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In this paper, using as model the theory of Lagrange geometry by R. Miron and the total space \(E=\bigoplus^ k_ 1TM\) of a vector bundle, the theory of \(k\)-Lagrange geometry for variational problems of multiple integrals is obtained. Since the metric is derived from a Lagrangian, the theory differs from \textit{Chr. Günther}'s theory [J. Differ. Geom.
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A Modification of Lagrange Interpolation
Acta Mathematica Hungarica, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xie, T., Zhou, X.
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On Reduction of Lagrange Systems
2010We consider nonlinear conservative Lagrange systems with cyclic coordinates, which by means of the Legendre transformation are reduced to linear Routh systems. The latter allows one to reduce the problem of qualitative analysis for the nonlinear systems of above type to linear systems.
Valentin Irtegov, Tatyana Titorenko
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On a Generalization of the Lagrange Function
American Journal of Physics, 1959Some mechanical aspects of a generalization with s-order derivatives of the Lagrange function are examined.
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Journal of Optimization Theory and Applications, 2001
This technical note is a valuable contribution to a historical problem of calculus and optimization theory. Its roots are due to Lagrange and Peano. A claim of Lagrange led to the hypothesis that a smooth function \(f:\mathbb{R}^n\to \mathbb{R}\) has a local minimum at \(x^*\) if all the directional derivatives of \(f\) at \(x^*\) are nonnegative ...
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This technical note is a valuable contribution to a historical problem of calculus and optimization theory. Its roots are due to Lagrange and Peano. A claim of Lagrange led to the hypothesis that a smooth function \(f:\mathbb{R}^n\to \mathbb{R}\) has a local minimum at \(x^*\) if all the directional derivatives of \(f\) at \(x^*\) are nonnegative ...
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On the Genesis of the Lagrange Multipliers
Journal of Optimization Theory and Applications, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Lagrange gamma distribution
Computational Statistics & Data Analysis, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Famoye, Felix, Govindarajulu, Z.
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On Lagrange Multipliers and Inequalities
Operations Research, 1961Necessary and sufficient conditions for minima (maxima) of nonlinear functionals subjected to linear constraints are derived. Two classes of functionals are considered (a) convex (concave) functionals for which necessary and sufficient conditions for global minima (maxima) are obtained, and (b) more general functionals possessing continuous second ...
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