Constraint Minimization-Pen and Paper Calculation

`f(x) = 5-(x-2)^2 - 2(y-1)^2`

       `5 - x^2-4+4x-2y^2-2+4y = 0`

       `-x^2-2y^2+4x+4y-1=0`

        

g(x)=f(x)+λ

`g(x) = -x^2-2y^2+4x+4y-1 + λ (x+4y-3)`

 

`(del g)/(del x)` = -2x+4+λ = 0  -----eq 1

`(del g)/(dely) = -4y+4+4λ`= 0 ------  eq2

`(del g)/(del λ) = x +4y-3 =0` -----    eq3

 

 

`-4y+4+4λ = 0 ---   eq2`

/4 in common

`-y+1+λ = 0`

`λ = y-1----- eq 4`

putting eq4  in eq 1 and 3

`-2x + y + 3 = 0------eq5`

`2x + 8y -6 = 0  ------eq6`

eq5/eq6

`-2x + y +3 = 0`

`2x + 8y - 6 = 0`

`-------------------`

       `9y - 3 = 0`

 

`y = 1/3`

`λ = (1/3)-1`

`λ = -2/3`

`-2x + y + 3 = 0`

`-2x + (1/3) =3 =0`

 

`x =5/3`

 


Projects by Sachin M

1.Objectives:      To compare the result of the base simulation and improve shell element properties. 2.Explanation :   2.1 Simulation 1 : First, 0000.rad file is imported to the Hypermesh. To get a minimum of 25 animation files, frequency is Read more

Objective:     The aim of this project is to do a geometry clean up for given models and perform 2D mesh using the midplane surface extract for the given parameters for the shell element. Procedure: Import the given model to Hypermesh --- Radioss. The Rad Read more

File Parsing using Python
Sachin M · 2019-09-14 04:42:56

Objective :    The aim of this project is do file parsing using python for different data provided in the file. Explanation:    File Parsing :         Text parsing is a common programming task that splits the given s Read more

Objective :      The main aim of the task is to perform a curve fit for linear and cubic polynomials equation and to find which curve fits the best to the actual data curve. Explanation :            The main aim of the cur Read more

Objective:   The main objective the process is to mesh the given hood model using ansa and do the hemming process at last. Hemming:    The hemming process is used in many automation where it helps to join two different surfaces with different material Read more

 Objective:       The main aim of this project is determining the minimum cushion pressure needed to break a given thickness of ice using an air cushion vehicle by breaking down the equation according to the Newton-Raphson technique. Introduction: Read more

Objective:  To write a program to simulate the transient behavior of a simple pendulum and to create an animation of its motion using python. Introduction:   In engineering, ODE(Ordinary Differential Equation) is used to describe the transient behavior of a Read more

AIM:    To plot PV diagram for the otto cycle and also computing thermal efficiency OBJECTIVE: Obtain values of pressure and volume of 4 points in the graph. Making an equation for the isentropic compression and expansion process Obtaining the thermal e Read more

Objective: To simulate the forward kinematics of a 2R Robotic Arm using Python. Procedure: Let, l1 and l2 be the length of the link1 and link 2 respectively. theta1 and theta2 be the angle made by the links 1 and 2 w.r.t horizontal. By assuming the theta1 and the Read more


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