Adaptive modification of objective function for lagrange multiplier method in constrained optimization problems

1993 ◽  
Vol 16 (2) ◽  
pp. 145-152
Author(s):  
Tsung‐Wu Lin ◽  
Jin‐Ten Huang ◽  
Ming‐Huei Joung
Keyword(s):  
Constrained Optimization ◽  
Objective Function ◽  
Lagrange Multiplier ◽  
Optimization Problems ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Constrained Optimization Problems ◽  
Adaptive Modification

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. 

ON RELIABILITY-BASED STRUCTURAL OPTIMISATION USING STOCHASTIC QUASIGRADIENT METHODS/ZUR ZUVERLÄSSIGKEITSTHEORETISCH GESTÜTZTEN TRAGWERKS-OPTIMIERUNG MIT VERFAHREN DER STOCHASTISCHEN QUASIGRA-DIENTEN

1995 ◽  
Vol 1 (2) ◽  
pp. 43-64
Author(s):  
E. R. Vaidogas
Keyword(s):  
Objective Function ◽  
Lagrange Multiplier ◽  
Failure Probability ◽  
Stochastic Gradient ◽  
Lagrange Multiplier Method ◽  
Time Dependent ◽  
Multiplier Method ◽  
Structural Failure ◽  
Structural Optimisation ◽  
Constraint Function

Methodical aspects of the reliability-based structural optimisation using stochastic quasigradient methods are considered. For an example of the simply supported reinforced concrete beam, the employment of the Lagrange multiplier method that belongs to the class of stochastic quasigradient methods is demonstrated. The classical optimum design goal to minimise structural cost or weight under the constraint on the structural failure probability is taken for consideration. Optimisation problems solved with the Lagrangemultiplier method are formulated in form of general stochastic programming problem. The mathematical expectation of the concrete volume reduced with respect to the in-place cost of the beam materials is taken as the objective function. Constraint function is the limitation placed on the beam failure probability. The beam is considered as a series structural system. Values of the prescribed allowable failure probability belongs to the interval in which the estimation of the failure probabilities by the simple Monte-Carlomethod is possible with an acceptable confidence. The time-independent case as well as the time-dependent one is considered in the optimisation problems. The generalisation on the time-dependent case is undertaken through the introduction into the constraint function of the quasi-linear distribution law of the random variables. In the time-dependent case, the objective function is associated with beginning and the constraint function with end of the service period. An expression of the stochastic gradient based on the differentiation under the integral sign is used for calculations with the Lagrange multiplier method. The stochastic gradient used is computationally more effective in comparison with stochastic finite-difference formulae usual in stochastic quasigradient methods because it requires only one computation of the structure in search iteration of the optimisation process. Three rules based on statistical argumentation are used for the stopping of the seat according to the procedure of the Lagrange multiplier method. The optimising of the beam shows that the Lagrange multiplier method is applicable for the optimal design of structures in that cases when the structural reliability can be estimated by means of the simple Monte-Carlo method. Additional research is needed for integration in the Lagrange multiplier method of statistical simulation techniques for the estimation of small structural failure probabilities.

Flexibility-Based Objective Functions for Constrained Optimization Problems on Structural Damage Detection

2011 ◽  
Vol 186 ◽  
pp. 383-387 ◽  
Author(s):  
Xi Chen ◽  
Ling Yu
Keyword(s):  
Damage Detection ◽  
Constrained Optimization ◽  
Objective Function ◽  
Structural Damage ◽  
Optimization Problems ◽  
Objective Functions ◽  
Structural Damage Detection ◽  
Constrained Optimization Problems ◽  
Modal Assurance Criterion ◽  
Damage Scenarios

Based on concepts of structural modal flexibility and modal assurance criterion (MAC), a new objective function is defined and studied for constrained optimization problems (COP) on structural damage detection (SDD) in this paper. Compared with traditionally objective function, which is defined based on natural frequencies and MAC, effect of objective functions on robustness of SDD calculation is evaluated through numerical simulation of a 2-storey rigid frame. Structural damages are identified by solving the COP on SDD based on an improved particle swarm optimization (IPSO) algorithm. Weak and multiple damage scenarios are mainly considered in various noise conditions. Some illustrated results show that the newly defined objective function is better than the traditional ones. It can be used to identify the damage locations but also to quantify the severity of weak and multiple damages in measurement noise conditions.

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.

Sign in / Sign up

Export Citation Format

Share Document