General Lagrange multiplier theorems

1974 ◽  
Vol 14 (1) ◽  
pp. 51-72 ◽  
Author(s):  
R. Weatherwax
Keyword(s):  
Lagrange Multiplier ◽  
Multiplier Theorems

scholarly journals ε-Properly Efficiency of Multiobjective Semidefinite Programming with Set-Valued Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Chun Hong Yuan ◽  
Wei Dong Rong
Keyword(s):  
Saddle Point ◽  
Semidefinite Programming ◽  
Lagrange Multiplier ◽  
Alternative Theorem ◽  
Generalized Cone Subconvexlikeness ◽  
Multiplier Theorems

In this paper, we study the ε-properly efficiency of multiobjective semidefinite programming with set-valued functions. Firstly, we obtain the scalarization theorems under the condition of the generalized cone-subconvexlikeness. Then, we establish the alternative theorem which contains matrixes and vectors, the ε-Lagrange multiplier theorems, and the ε-proper saddle point theorems of the primal programming under some suitable conditions.

scholarly journals Use of the Lagrange Multiplier Test for Assessing Measurement Invariance Under Model Misspecification

2021 ◽  
pp. 001316442110203
Author(s):  
Lucia Guastadisegni ◽  
Silvia Cagnone ◽  
Irini Moustaki ◽  
Vassilis Vasdekis
Keyword(s):  
Lagrange Multiplier ◽  
False Positive ◽  
Latent Variable ◽  
Model Misspecification ◽  
Cross Product ◽  
Small Sample ◽  
Type I ◽  
Local Dependence ◽  
Lagrange Multiplier Test ◽  
Product Approach

This article studies the Type I error, false positive rates, and power of four versions of the Lagrange multiplier test to detect measurement noninvariance in item response theory (IRT) models for binary data under model misspecification. The tests considered are the Lagrange multiplier test computed with the Hessian and cross-product approach, the generalized Lagrange multiplier test and the generalized jackknife score test. The two model misspecifications are those of local dependence among items and nonnormal distribution of the latent variable. The power of the tests is computed in two ways, empirically through Monte Carlo simulation methods and asymptotically, using the asymptotic distribution of each test under the alternative hypothesis. The performance of these tests is evaluated by means of a simulation study. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the tests performance deteriorates, especially for false positive rates under local dependence and power for small sample size under misspecification of the latent variable distribution. In general, the Lagrange multiplier test computed with the Hessian approach and the generalized Lagrange multiplier test have better performance in terms of false positive rates while the Lagrange multiplier test computed with the cross-product approach has the highest power for small sample sizes. The asymptotic power turns out to be a good alternative to the classic empirical power because it is less time consuming. The Lagrange tests studied here have been also applied to a real data set.

System Energy Efficiency Comparison of AC and DC Buildings Based on Lagrange Multiplier

2021 ◽  
Author(s):  
Xinliang Yang ◽  
Hanju Ding ◽  
Yanda Lv ◽  
Yuanyuan Lu ◽  
Yuming Zhao ◽  
...  
Keyword(s):  
Energy Efficiency ◽  
Lagrange Multiplier ◽  
System Energy ◽  
Efficiency Comparison
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