Optimization Techniques

This course is meant for exposing the students to the mathematical details of the techniques for obtaining optimum solutions under constraints for desired output. They will be taught numerical methods of optimization, linear programming techniques, nonlinear programming and multiple  programming. Students will also be exposed to practical applications of these techniques.

 

  • Classical and numerical methods of optimization - Constrained optimization, Lagrange multipliers, Necessary Conditions for an Extremum. Statistical Applications. Optimization and Inequalities. Classical Inequalities, like Cauchy-Schwarz Inequality, Jensen Inequality and Markov Inequality. 
  • Numerical Evaluation of Roots of Equations, Sequential Search Methods - Fibonacci Search Method.  Random Search Method – Method of Hooke and Jeeves, Simplex Search Method.  Gradient Methods, like Newton’s Method and Method of Steepest Ascent. 
  • Linear programming techniques, Simplex method, Karmarkar’s algorithm, Duality and Sensitivity analysis, Zero-sum Two-person Finite Games and Linear Programming.  Integer Programming.  Statistical Applications.
  • Nonlinear programming, Kuhn-Tucker sufficient conditions, Elements of multiple  programming, Dynamic Programming, Optimal control theory - Pontryagin’s maximum principle, Time-optimal control problems. Quadratic Programming. 

Problems based on optimization techniques with constraints, Minimization problems using numerical methods. Linear programming (LP) problems through graphical method. LP problem using simplex method (Two-phase method). LP problem using primal and dual method, Sensitivity analysis for LP problem. LP problem using Karmarkar’s method, Problems based on Quadratic programming. Problems based on Integer programming, Problems based on Dynamic programming. Problems based on Pontryagin’s Maximum Principle.