Course

Unit I

Introduction to LPP: Lines and hyperplanes, Convex sets, Convex hull, Formulation of a Linear Programming Problem, Linear Programming Problem; Graphical Method; Simplex method; Dual problem, Duality theory, Dual simplex method, Revised simplex method.

Unit II

Introduction to optimization: classical optimization, Optimality criteria – Necessary and sufficient conditions for existence of optimum point. Fundamental Region Elimination Rules to eliminate a region. One dimensional Search methods: Golden search method, Fibonacci method, Newton’s Method, Secant Method, Remarks on line Search Sections.

Unit III

Unconstrained Multivariable optimization: Introduction, Necessary and sufficient conditions for existence of extreme point. Conditions for local minimization. Direct search methods: unidirectional search, box evolutionary search method.

Unit IV

Gradient-based methods- introduction, the method of steepest descent, analysis of Gradient Methods, Convergence, Convergence Rate. Analysis of Newton’s Method, Newton’s Method for Nonlinear Least-Squares. Introduction -The Conjugate Direction Algorithm, The Conjugate Gradient Algorithm for unconstrained optimization problems.

Unit V

Nonlinear Equality Constrained Optimization- Introduction, Problems with equality constraints Problem Formulation, Lagrange Multiplier Method – Nonlinear Inequality Constrained Optimization: – Problems with inequality constraints: Kuhn-Tucker conditions. Specific Search Algorithms: Hill Climbing, Simulated Annealing, Genetic Algorithms, Ant Colony Optimization.

CO1: To learn Linear Programming Problems.

CO2: To learn single variable optimization techniques

CO3: To understand the basics of unconstrained optimization problems and direct search, unidirection search methods for multivariable problems.

CO4: To learn the various unconstrained optimization techniques for multivariable.

CO5: To understand and solve the nonlinear optimization problem with equality and inequality constrained problems and to learn theory of few significant genetic

evolutionary algorithms. 

CO-PO Mapping:

Text Books/ Reference Books:

1. Edwin K.P. Chong, Stanislaw H. Zak, “An Introduction to Optimization”, 2^nd edition, Wiley, 2013.
2. Mokhtar S. Bazarra, Hamit D Sherali, C.M. Shetty, “Nonlinear programming Theory and applications”, 2^nd edition, Wiley , 2004.
3. Mohan C. Joshi and Kannan M. Moudgalya, Optimization: Theory and Practice, Narosa Publishing House, New Delhi, 2004 (Reference)
4. Kalyanmoy Deb, “Optimization for Engineering Design Algorithms and Examples”, Prentice Hall of India, New Delhi, 2004.
5. S. Rao, “Optimization Theory and Applications”, Second Edition, New Age International (P) Limited Publishers, 1995.
6. Bertsimas, Dimitris, and John Tsitsiklis. Introduction to Linear Optimization. Belmont, MA: Athena Scientific, 1997.