Optimization Techniques

Process optimization, Formulation of various process optimization problems and their classification, Basic concepts of optimization-convex and concave functions, Necessary and sufficient conditions for stationary points.

Unconstrained multivariable optimization direct search methods, Bracketing methods: Exhaustive search, Bounding phase, Region elimination methods- Interval halving, Fibonacci search, Golden section search, Point Estimation, Successive quadratic estimation methods.

Gradient-based methods-Newton Raphson, Bisection, Secant, Cubic spline, Root-finding using optimization Techniques.

Optimality criteria, Unidirectional search, Direct search Methods- Evolutionary optimization, Simplex search, Powell’s conjugate direction, Gradient-based methods- Cauchy’s (steepest descent) method, Newton’s method.

Kuhn-Tucker conditions, Transformation methods, Penalty function method, Method of multipliers, Sensitivity analysis, Direct search for constraint Minimization-Variable elimination method Advanced techniques for optimization