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LAGRANGE MULTIPLIERS IN INTRINSIC ELASTICITY
Mathematical Models and Methods in Applied Sciences, 2011In an intrinsic approach to three-dimensional linearized elasticity, the unknown is the linearized strain tensor field (or equivalently the stress tensor field by means of the constitutive equation), instead of the displacement vector field in the classical approach.
Iosifescu, Oana +4 more
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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 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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Journal of Optimization Theory and Applications, 1980
Solutions of constrained minimization problems give rise to Lagrange multiplier rules. In this paper, we show that a simple condition on a specific constraint implies that the associated coefficient in the Lagrange multiplier rule is not zero. We conclude with an example which shows that such knowledge increases the information available about the ...
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Solutions of constrained minimization problems give rise to Lagrange multiplier rules. In this paper, we show that a simple condition on a specific constraint implies that the associated coefficient in the Lagrange multiplier rule is not zero. We conclude with an example which shows that such knowledge increases the information available about the ...
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Vector maximisation and lagrange multipliers
Mathematical Programming, 1985This paper deals with the characterization of the efficient set of a set \(Z\subseteq {\mathbb{R}}^ n\), further constrained by constraints \(g_ k(x)\leq 0\), \(1\leq k\leq p\), with respect to a multiple objective vector function \(f: {\mathbb{R}}^ n\to {\mathbb{R}}^ m\).
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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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A New Approach to Lagrange Multipliers
Mathematics of Operations Research, 1976We consider a mathematical programming problem on a Banach space, and we derive necessary conditions for optimality in Lagrange multiplier form. We prove further that “most mathematical programming problems are normal.” The novelty of our approach lies on the one hand in the absence of both differentiability and convexity hypotheses on the functions ...
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Geometric Programming: Estimation of Lagrange Multipliers
Operations Research, 1985This paper presents a method for estimating Lagrange multipliers for generalized Geometric Programming. The Lagrange multipliers of a linearized problem serve as estimates of the generalized Geometric Programming multipliers.
M. J. Rijckaert, E. J. C. Walraven
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A note on an approximate lagrange multiplier rule
Mathematical Programming, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Joydeep Dutta +2 more
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On the method of Lagrange multiplier and others
Acta Mechanica Sinica, 1986The fundamentals for the correct use of the method of Lagrange multipliers are presented and illustrated by examples. It is pointed out that for a given problem of mechanics, there may be many equivalent and unequivalent variational principles. The functionals of the so-called generalized variational principles of elasticity are linear combinations of ...
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