Multiple Lagrange Multiplier Method for Constrained Evolutionary Optimization

2000 ◽  
Vol 4 (2) ◽  
pp. 158-163 ◽  
Author(s):  
Hyun Myung ◽  
◽  
Jong-Hwan Kim ◽  
Keyword(s):  
Lagrange Multiplier ◽  
Optimization Problem ◽  
Evolutionary Programming ◽  
Optimization Techniques ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Evolutionary Search ◽  
Two Phase ◽  
Global Optima ◽  
Sharing Function

One of the well-known problems in evolutionary search for solving optimization problem is the premature convergence. The general constrained optimization techniques such as hybrid evolutionary programming, two-phase evolutionary programming, and Evolian algorithms are not safe from the same problem in the first phase. To overcome this problem, we apply the sharing function to the Evolian algorithm and propose to use the multiple Lagrange multiplier method for the subsequent phases of Evolian. The method develops Lagrange multipliers in each subpopulation region independently and seeks for multiple global optima, if any, in parallel. The simulation results demonstrate the usefulness of the proposed multiple Lagrange multiplier method.

scholarly journals Sensitivity functionals in convex optimization problem

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3681-3687
Author(s):  
Robert Namm ◽  
Gyungsoo Woo
Keyword(s):  
Variational Inequality ◽  
Convex Optimization ◽  
Lagrange Multiplier ◽  
Optimization Problem ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Convex Optimization Problem ◽  
Infinite Dimensional ◽  
Finite Dimensional

We consider sensitivity functionals and Lagrange multiplier method for solving finite dimensional convex optimization problem.An analysis based on this property is also applied for semicoercive infinite dimensional variational inequality in mechanics.

scholarly journals Application of Lagrange Multiplier Method for Computing Fold Bifurcation Point in A Two-Prey One Predator Dynamical System

2018 ◽  
Vol 24 (2) ◽  
pp. 7-19
Author(s):  
Marwan Marwan ◽  
Johan Matheus Tuwankotta ◽  
Eric Harjanto
Keyword(s):  
Dynamical System ◽  
Lagrange Multiplier ◽  
Bifurcation Point ◽  
Optimization Problem ◽  
The Other ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Constrained Optimization Problem ◽  
Fold Bifurcation ◽  
The Cost

We propose by means of an example of applications of the classical Lagrange Multiplier Method for computing fold bifurcation point of an equilibrium ina one-parameter family of dynamical systems. We have used the fact that an equilibrium of a system, geometrically can be seen as an intersection between nullcline manifolds of the system. Thus, we can view the problem of two collapsing equilibria as a constrained optimization problem, where one of the nullclines acts as the cost function while the other nullclines act as the constraints.

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 Lagrange Multiplier Method for Drilling Oil Reservoir

2017 ◽  
Vol 06 (03) ◽  
Author(s):  
Vasant P ◽  
Maung MT ◽  
Min YW ◽  
Tun HM ◽  
Thant KZ
Keyword(s):  
Lagrange Multiplier ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Oil Reservoir
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