scholarly journals Lagrange Multiplier Tests in Applied Research

2020 ◽  
Vol 12 (1) ◽  
pp. 13-19 ◽  
Author(s):  
José Gabriel Astaiza-Gómez
Keyword(s):  
Constrained Optimization ◽  
Hypothesis Testing ◽  
Lagrange Multiplier ◽  
Applied Research ◽  
Asymptotic Theory ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Lagrange Multiplier Test ◽  
Constrained Optimization Problems ◽  
Lagrange Multiplier Tests

Applied research requires the usage of the proper statistics for hypothesis testing. Constrained optimization problems provide a framework that enables the researcher to build a statistic that fits his data and hypothesis at hand. In this paper I show some of the necessary conditions to obtain a Lagrange Multiplier test as well as some popular applications in order to highlight the usefulness of the test when the researcher must rely in asymptotic theory and to help the reader in the construction of a test in applied work.

scholarly journals Analisis Karakteristik Fungsi Lagrange Dalam Menyelesaikan Permasalahan Optimasi Berkendala

2018 ◽  
Vol 1 (1) ◽  
pp. 037-043
Author(s):  
Theresia Mehwani Manik ◽  
Parapat Gultom ◽  
Esther Nababan
Keyword(s):  
Constrained Optimization ◽  
Objective Function ◽  
Lagrange Multiplier ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Quadratic Function ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Objective Functions ◽  
Constrained Optimization Problems

Optimasi adalah suatu aktivitas untuk mendapatkan hasil terbaik di dalam suatu keadaan yang diberikan. Tujuan akhir dari aktivitas tersebut adalah meminimumkan usaha (effort) atau memaksimumkan manfaat (benefit) yang diinginkan. Metode pengali Lagrange merupakan metode yang digunakan untuk menangani permasalahan optimasi berkendala. Pada penelitian ini dianalisis karakteristik dari metode pengali Lagrange sehingga metode ini dapat menyelesaikan permasalahan optimasi berkendala. Metode tersebut diaplikasikan pada salah satu contoh optimasi berkendala untuk meminimumkan fungsi objektif kuadrat sehingga diperolehlah nilai minimum dari fungsi objektif kuadrat adalah -0.0403. Banyak masalah optimasi tidak dapat diselesaikan dikarenakan kendala yang membatasi fungsi objektif. Salah satu karakteristik dari metode pengali Lagrange adalah dapat mentransformasi persoalan optimasi berkendala menjadi persoalan optimasi tanpa kendala. Dengan demikian persoalan optimasi dapat diselesaikan.   Optimization is an activity to get the best results in a given situation. The ultimate goal of the activity is to minimize the effort or maximize the desired benefits. The Lagrange multiplier method is a method used to handle constrained optimization problems. This study analyzed the characteristics of the Lagrange multiplier method with the aim of solving constrained optimization problems. The method was applied to one sample of constrained optimization to minimize the objective function of squares and resulted -0.0403 as the minimum value of the objective quadratic function. Many optimization problems could not be solved due to constraints that limited objective functions. One of the characteristics of the Lagrange multiplier method was that it could transform constrained optimization problems into non-constrained ones. Thus the optimization problem could be resolved. 

scholarly journals A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhijun Luo ◽  
Lirong Wang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Descent Direction ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Globally Convergent ◽  
Variable Distribution ◽  
Systems Of Linear Equations

A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

Sign in / Sign up

Export Citation Format

Share Document