PPO Multivariable optimization

Multidimensional
Nonlinear Optimization Unconstrained Problems (figure, formulation,analytical
solution), +ves and alternatives)

Describe in short
some direct methods

Describe the
abstract scheme for indirect methods

Steepest descent
method(+ves and -ves)

Newton's
method(+ves and -ves) 

Quasi Newton's
method(+ves and -ves) 

Conjugate gradient
method and advantages?

Problems with
Equality Constraints-General formulation and reduced gradient method.
Possible problems

Lagrange
multipliers-sufficient conditions, necessary conditions and sensitivity
analysis

Problems with
Inequality Constraints and Kuhn tucker conditions.