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• To make students learn about linear programming models.
• To make students learn about mathematical concepts of optimization techniques.
• Introduce students to various optimization problems.

• Understand importance of optimization of industrial process management.
• Apply basic concepts of mathematics to formulate an optimization problem.
• Analyse and appreciate variety of performance measures for various optimization problems.

(12 Hours)

Convex sets and convex functions, Kuhn-Tucker conditions. convex optimization, Convex quadratic programming: Wolfe's and Pivot complementary algorithms. Separable programming, Lagrange multipliers, Non-linear programming: One-dimensional minimization method, search method, unconstrained and constrained optimization theory and practices.

Basic concepts, conditional failure rate function, Failure time distributions, Certain life models, Reliability of a system in terms of the reliability of it's components, series system, Parallel system.

(06 Hours)

Introduction - Graphical solution; Graphical sensitivity analysis- The standard form of linear programming problems - Basic feasible solutions -unrestricted variables - simplex algorithm - artificial variables - Big M and two phase method - Degeneracy - alternative optima - unbounded solutions - infeasible solutions.

(06 Hours)

Discrete and continuous dynamic programming (simple illustrations). Multistage decision problems, computation procedure and case studies. Fundamentals of queuing system, Poisson process, the birth and death process, special queuing methods. Recursive nature of dynamic programming - Forward and Backward Recursion.

(06 Hours)

Unimodal functions, simultaneous uniform search method, Sequential search method, Fibonacci search method, Golden section search method.

(04 Hours)

Univariate search method, Method of steepest descent, Conjugate radient method, Fletcher Reeves method.

(04 Hours)

Rosen's Gradient projection method, Penalty function method.

(04 Hours)

Two person Zero Sum Games - Mixed strategy games and their algorithms.

(14 Hours)

(Total Contact Time: 42 Hours + 14 Hours = 56 Hours)

1. Wenyu Sun, Ya-Xiang Yuan, Optimization Theory and Methods: Nonlinear Programming, Springer, 2006.
2. Stephen Boyd, LievenVandenberghe, Convex Optimization, Cambridge University Press, 2004.
3. A. Ravindran, K. M. Ragsdell, G. V. Reklaitis, Engineering Optimization: Methods and Applications, Second Edition, Wiley, 2007.
4. Godfrey C. Onwubolu, B. V. Babu, New Optimization Techniques in Engineering, Springer, 2004.
5. SergiyButenko, Panos M. Pardalos, Numerical Methods and Optimization: An Introduction, CRC, 2014.