Lagrange Multipliers and Lower Bounds for Integral Functionals

Emmanuel Giner

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Lagrange Multipliers and Lower Bounds for Integral Functionals

机译：拉格朗日乘子和积分的下界

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摘要

We present a large class of examples with the remarkable property pointed out by Professor B. Ricceri (see [13], [14], [15]), about lower bounds of integral functionals. We use only a Lagrange duality result contained in [5].

机译：我们提供了B. Ricceri教授（参见[13]，[14]，[15]）指出的有关非整数函数下界的大量示例。我们仅使用[5]中包含的拉格朗日对偶结果。

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《Journal of convex analysis》 |2010年第1期|共8页
作者
Emmanuel Giner;
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正文语种 eng
中图分类数学分析;
关键词
Decomposability; richness; essential infimum; measurable integrand; integral functional; duality; Lagrange multipliers;

机译：可分解性;丰富性;本质上的不足;可测量的被积分数;积分泛函;对偶性;拉格朗日乘数;

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专利

1. Lagrange Multipliers and Lower Bounds for Integral Functionals [J] . Emmanuel Giner Journal of convex analysis . 2010,第1期

机译：拉格朗日乘子和积分的下界
2. Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation [J] . Dal Maso Gianni, Orlando Gianluca, Toader Rodica Advances in Calculus of Variations . 2017,第2期

机译：界限变形功能空间的一类积分功能的半连续性
3. Lower Semicontinuity for Integral Functionals in the Space of Functions of Bounded Deformation Via Rigidity and Young Measures [J] . Rindler F. Archive for Rational Mechanics and Analysis . 2011,第1期

机译：刚度和杨氏测界在有界变形函数空间中积分泛函的下半连续性
4. A Parallel Computing Procedure for the Lower and Upper Bounds on the Functionals of Solutions to PDE: Application to the J-Integral in Functionally Graded Materials [C] . Xuan Z.C. 2011 Fourth International Symposium on Parallel Architectures, Algorithms and Programming . 2011

机译：PDE解的功能上下界的并行计算过程：在功能梯度材料中的J积分应用
5. Finding Displacements Using Castigliano’s Theorem, LaGrange Multipliers, Heaviside Step Functions, and Numerical Integration [D] . ?Gallegos, Selso 2020

机译：使用Castigliano定理，拉格朗日乘法器，沉重阶段函数和数字集成来寻找位移
6. Physics successfully implements Lagrange multiplier optimization [O] . Sri Krishna Vadlamani, Tianyao Patrick Xiao, Eli Yablonovitch 2020

机译：物理成功实现拉格朗日乘数优化
7. Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures [O] . Rindler, Filip 2011

机译：在函数空间中对积分函数的半连续性较低通过刚度和杨氏测量的有界变形
8. Computable Numerical Bounds for Lagrange Multipliers of Stationary Points of Nonconvex Differentiable Nonlinear Programs [R] . Mangasarian, O. L. 1985

机译：非凸可微非线性程序平稳点Lagrange乘子的可计算数值界

Lagrange Multipliers and Lower Bounds for Integral Functionals

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