Constrained Optimization

OBJECTIVE: In this challenge, we will find minimum value of the given function which is constrained by other function.



`f(x,y)=5-(x-2)^2-2(y-1)^2` constrained to `x+4y=3`


`g(x,y)=5-(x-2)^2 -2(y-1)^2+lamda(x+4y-3)`


`implies -2(x-2)+lamda=0`----->(A)


`implies -4(y-1)+4y =0`

`implies-(y-1)+y =0`-------->(B)



from equation (A) and(B)


`implies 2x-y=3`----->(D)

from equation (C) AND (D)


`implies x=5y`

putting `x=5y` in equation (C), we get`9y =3`

`impliesy= (1/3)`-----(1)

`implies x= (5/3)`-----(2)

as`lamda = (y-1); implies lamda= (-2/3)`----->(3)

The minimum value of given function:

`f(x,y)=5-(x-2)^2-2(y-1)^2` is at `x=(5/3) and y=(1/3)`




Projects by LUV KUMAR

OBJECTIVE: To simulate the side crash analysis of the given neon model. STEPS: UNIT SYSTEM: During whole analysis, Kg KN mm ms was followed. INTERFACES: Deleted already defined interfaces and created Type 7 global interface. The properties for the Type 7 interface a Read more

LUV KUMAR · 2019-10-31 04:05:45

OBJECTIVE: To perform a frontal crash simulation using Radioss as a solver. STEPS: View components: In the NEON FRONT model there are 75 components. ASSIGNING MATERIAL ID, PROPERTY ID, AND CARD IMAGE: For rigid bodies, card image is none and prop id, mat id is uns Read more

OBJECTIVE: Studying Interfaces and boundary condition in Hypercrash, Hypermesh and meshing bumper assembly MESHING OF BUMPER ASSEMBLY: Topological error like faces not connected was removed using extend option under surface edit option. Auto mesh under 2D option wa Read more

OBJECTIVE: Through this challenge, we will study different material laws in Radioss and will select the best material law for the given scenario by simulating and plotting graph. STEPS CASE1: Changing the model name from FAILURE_JOHNSON_0000 to Law2_epsmax_failure.R Read more

OBJECTIVE: To compare the results with base simulation and improved shell elements properties by performing energy, mass error checks, plotting graph in HyperGraph and animating in HyperView. SIMULATION 1: With default Shell Properties. Imported Element_Formulati Read more

OBJECTIVE: To clean the geometry, extract mid surface, mesh the extracted surface and assign thickness to given models. LINK TO HYPERMESH FILES   PROCEDURE: Model was imported and to see Read more

OBJECTIVE: Surface mesh and volume mesh generation on given housing and arm bracket model. LINK TO HYPER MESH RADIOSS FILES: 3D MESHING: 3D Elements should be used when all dimensions are compara Read more

LUV KUMAR · 2019-09-13 07:11:16

OBJECTIVE: To find minimum pressure using Newton-Raphson method PROGRAMMING EXPLAINED: Two functions are defined. f and fprime. These function are defined to calculate next iteration value using NR method. To calculate pressure values for different thickness, for a Read more

File Parsing in Python
LUV KUMAR · 2019-09-13 06:25:32

OBJECTIVE: To demonstate file parsing using Python. when we run the program, first thing appears is  to enter the filename,if we speicify correct name then we can see the rest output otherwise a message will show file not found. To store different properties li Read more

SciPy Curve Fitting
LUV KUMAR · 2019-09-12 14:32:22

OBJECTIVE: To curve fit given data using linear and cubic polynomial. For curve fitting, we imported curve_fit from scipy library. Defined two function, func and func1 which are used for fitting curve. Defined another function read_file to read temperature and cp v Read more


The End