Write a note on Matrix inversion technique based on Cholesky decomposition.

Discuss in detail the utility and application of the principle of virtual work in Structural Analysis.

2. Check whether the point is a local minimum of the problem:
f x1 x2 x3
g1=8 x1^2 x2^2
g2 x3 4
g3=x2 8
gl,g2,g3 0

3. Differentiate between sizing, shape and topology optimisation of structures.

Write a short note on convergence criteria for iterative methods.

Write a note on perturbation and sensitivity analysis.

5. Consider a problem of the form

Minimize subject to fi i ...., n
Ax b

where, fo, f1,... fn are convex and the domain of the objective function is defined as € dom fo c^Tx d 0}.

For this, show that this is a quasiconvex optimisation problem.

6. Solve the following set. of equations by Gauss elimination method:
-3y 7z 2
x 2y z
5x -2y 2

7. Find the minimum of
f 2x2^2 10x1 6 2x2^3
subject to
g1 10-x1x2
g2 =x1
g3 10 x2
gl,g2,g3 0

The Kuhn-Tucker conditions are

-3x1^2 10 +A1x2

-4x2 6x2^2 A1X1 Ag =0.