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1970
The classical instances of saddle point theorems are the minimax theorems of v. Neumann [1] (6.1.1) and Kakutani [3]. Since then the saddle point concept has been found to apply in a much larger context. It is also a natural and rich source for duality theorems.
Josef Stoer, Christoph Witzgall
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The classical instances of saddle point theorems are the minimax theorems of v. Neumann [1] (6.1.1) and Kakutani [3]. Since then the saddle point concept has been found to apply in a much larger context. It is also a natural and rich source for duality theorems.
Josef Stoer, Christoph Witzgall
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1980
Publisher Summary This chapter presents a simple critical point theorem for certain indefinite functionals. The result follows from a theorem by Ekeland on the minimization of non-convex functionals and provides a generalization of a recent minimax theorem due to Lazer, Landesman, and Meyers. The advantages of the Ekeland theorem over the main result
Peter W. Bates, Ivar Ekeland
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Publisher Summary This chapter presents a simple critical point theorem for certain indefinite functionals. The result follows from a theorem by Ekeland on the minimization of non-convex functionals and provides a generalization of a recent minimax theorem due to Lazer, Landesman, and Meyers. The advantages of the Ekeland theorem over the main result
Peter W. Bates, Ivar Ekeland
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The Arabian journal for science and engineering, 2021
K. Gangadhar +3 more
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K. Gangadhar +3 more
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2016
Standard numerical methods fail to provide accurate approximations when partial differential equations involve constraints defined by a differential operator or when they contain terms weighted by a larger parameter. Generalizations of the Lax–Milgram and Cea lemmas provide a concise framework for the development and analysis of appropriate numerical ...
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Standard numerical methods fail to provide accurate approximations when partial differential equations involve constraints defined by a differential operator or when they contain terms weighted by a larger parameter. Generalizations of the Lax–Milgram and Cea lemmas provide a concise framework for the development and analysis of appropriate numerical ...
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Nonlinear Analysis: Theory, Methods & Applications, 2005
From the beginning of the calculus of variations over 300 years ago, scientists were interested in finding extrema of expressions (now called functionals) involving unknown functions. It was discovered that functions producing extrema are solutions of differential equations (called Euler equations).
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From the beginning of the calculus of variations over 300 years ago, scientists were interested in finding extrema of expressions (now called functionals) involving unknown functions. It was discovered that functions producing extrema are solutions of differential equations (called Euler equations).
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1971
In this section, we consider the linear system $${\rm{\dot u}}\left( {\rm{t}} \right) = {\rm{L}}\left( {{\rm{u}}_{\rm{t}} } \right)$$ (26.1) and the perturbed linear system $${\rm{\dot x}}\left( {\rm{t}} \right) = {\rm{L}}\left( {{\rm{x}}_{\rm{t}} } \right) + {\rm{f}}\left( {{\rm{x}}_{\rm{t}} } \right)$$ (26.2) where $${\rm{L ...
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In this section, we consider the linear system $${\rm{\dot u}}\left( {\rm{t}} \right) = {\rm{L}}\left( {{\rm{u}}_{\rm{t}} } \right)$$ (26.1) and the perturbed linear system $${\rm{\dot x}}\left( {\rm{t}} \right) = {\rm{L}}\left( {{\rm{x}}_{\rm{t}} } \right) + {\rm{f}}\left( {{\rm{x}}_{\rm{t}} } \right)$$ (26.2) where $${\rm{L ...
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Iterative Saddle Point Techniques
SIAM Journal on Applied Mathematics, 1967Iterative solution methods for minimizing convex, differentiable function in Euclidean ...
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Approximation of Saddle Point Problems
1991This chapter is in a sense the kernel of the book. It sets a general framework in which mixed and hybrid finite element methods can be studied. Even if some applications will require variations of the general results, these could not be understood without the basic notions introduced here. Our first concern will be existence and uniqueness of solutions.
Daniele Boffi +2 more
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Note on ε-saddle point and saddle point theorems
Acta Mathematica Hungarica, 1994Xian-Zhi Yuan, Jian Yu, Kok-Keong Tan
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Variable parameter Uzawa method for solving a class of block three-by-three saddle point problems
Numerical Algorithms, 2020Na Huang
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